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An ordinary [[Equivariant cohomology|equivariant cohomology]] for a finite group <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b1108701.png" />, defined in [[#References|[a1]]], on the [[Category|category]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b1108702.png" />-CW of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b1108704.png" />-complexes (cf. [[Complex|Complex]]; [[CW-complex|CW-complex]]). The objects of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b1108705.png" />-CW are the CW-complexes <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b1108706.png" /> with a cellular action of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b1108707.png" />, satisfying the condition that, for every subgroup <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b1108708.png" /> of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b1108709.png" />, the fixed point set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087010.png" /> is a subcomplex of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087011.png" />. The morphisms are the cellular <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087012.png" />-mappings. Let <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087013.png" /> be the full subcategory of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087014.png" />-CW whose objects are the <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087015.png" />-orbits <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087016.png" />, where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087017.png" /> is a subgroup of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087018.png" />. For every contravariant [[Functor|functor]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087019.png" /> from <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087020.png" /> to the category <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087021.png" /> of Abelian groups, there exists a Bredon cohomology theory <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087022.png" /> which, after restriction to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087023.png" />, vanishes for <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087024.png" /> and is equal to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087025.png" /> for <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087026.png" />.
+
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Let <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087027.png" /> be the chain [[Complex|complex]] of functors from <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087028.png" /> to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087029.png" /> such that, for every subgroup <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087030.png" /> of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087031.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087032.png" /> is the ordinary cellular chain complex of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087033.png" />. Then
+
{{TEX|auto}}
 +
{{TEX|done}}
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087034.png" /></td> </tr></table>
+
An ordinary [[Equivariant cohomology|equivariant cohomology]] for a finite group  $  G $,
 +
defined in [[#References|[a1]]], on the [[Category|category]]  $  G $-
 +
CW of  $  G $-
 +
complexes (cf. [[Complex|Complex]]; [[CW-complex|CW-complex]]). The objects of  $  G $-
 +
CW are the CW-complexes  $  X $
 +
with a cellular action of  $  G $,
 +
satisfying the condition that, for every subgroup  $  H $
 +
of  $  G $,
 +
the fixed point set  $  X  ^ {H} $
 +
is a subcomplex of  $  X $.  
 +
The morphisms are the cellular  $  G $-
 +
mappings. Let  $  O _ {G} $
 +
be the full subcategory of  $  G $-
 +
CW whose objects are the  $  G $-
 +
orbits  $  G/H $,
 +
where  $  H $
 +
is a subgroup of  $  G $.  
 +
For every contravariant [[Functor|functor]]  $  M $
 +
from  $  O _ {G} $
 +
to the category  $  { \mathop{\rm Ab} } $
 +
of Abelian groups, there exists a Bredon cohomology theory  $  \{ H  ^ {n} _ {G} ( -,M ) \} _ {n \in \mathbf N }  $
 +
which, after restriction to  $  O _ {G} $,
 +
vanishes for  $  n > 0 $
 +
and is equal to  $  M $
 +
for  $  n = 0 $.
  
where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087035.png" /> denotes the set of natural transformations of functors. The functors <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087036.png" /> are projective objects in the [[Category|category]] of coefficient systems and there is a [[Spectral sequence|spectral sequence]]
+
Let  $  c _ {*} ( X ) $
 +
be the chain [[Complex|complex]] of functors from  $  O _ {G} $
 +
to  $  { \mathop{\rm Ab} } $
 +
such that, for every subgroup  $  H $
 +
of  $  G $,
 +
$  c _ {*} ( X ) ( G/H ) = C _ {*} ( X  ^ {H} ) $
 +
is the ordinary cellular chain complex of  $  X  ^ {H} $.
 +
Then
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087037.png" /></td> </tr></table>
+
$$
 +
H  ^ {n} _ {G} ( X,M ) = H  ^ {n} ( { \mathop{\rm Hom} } _ {O _ {G}  } ( c _ {*} ( X ) ,M ) ) ,
 +
$$
  
where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087038.png" />.
+
where $  { \mathop{\rm Hom} } _ {O _ {G}  } ( -, - ) $
 +
denotes the set of natural transformations of functors. The functors  $  c _ {n} ( X ) $
 +
are projective objects in the [[Category|category]] of coefficient systems and there is a [[Spectral sequence|spectral sequence]]
  
Let <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087039.png" /> be a <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087040.png" />-space with base point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087041.png" /> (cf., e.g., [[Equivariant cohomology|Equivariant cohomology]]). Important examples of coefficient systems are the [[Homotopy|homotopy]] group functors <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087042.png" /> defined by <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087043.png" />. The [[Obstruction|obstruction]] theory for <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087044.png" />-mappings <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087045.png" /> is formulated in terms of the cohomology groups <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087046.png" />. For any coefficient system <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087047.png" /> and natural number <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087048.png" />, there is a pointed Eilenberg–MacLane <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087050.png" />-complex <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087051.png" /> such that <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087052.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087053.png" /> vanishes whenever <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087054.png" />. For every <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087055.png" />-complex <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087056.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087057.png" />, where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087058.png" /> denotes <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087059.png" />-homotopy classes of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087060.png" />-mappings.
+
$$
 +
{ \mathop{\rm Ext} }  ^ {p} _ {O _ {G}  } ( h _ {q} ( X ) ,M ) \Rightarrow H ^ {p + q } _ {G} ( X,M ) ,
 +
$$
  
If <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087061.png" /> is an equivariant cohomology theory defined on the category <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087062.png" />-CW, then there exists an Atiyah–Hirzebruch-type spectral sequence
+
where  $  h _ {q} ( X ) ( G/H ) = H _ {q} ( X  ^ {H} ) $.
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087063.png" /></td> </tr></table>
+
Let  $  Y $
 +
be a  $  G $-
 +
space with base point  $  y _ {0} $(
 +
cf., e.g., [[Equivariant cohomology|Equivariant cohomology]]). Important examples of coefficient systems are the [[Homotopy|homotopy]] group functors  $  \pi _ {n} ( Y ) $
 +
defined by  $  \pi _ {n} ( Y ) ( G/H ) = \pi _ {n} ( Y  ^ {H} ,y _ {0} ) $.
 +
The [[Obstruction|obstruction]] theory for  $  G $-
 +
mappings  $  f : X \rightarrow Y $
 +
is formulated in terms of the cohomology groups  $  H  ^ {n} _ {G} ( X, \pi _ {m} ( Y ) ) $.
 +
For any coefficient system  $  M $
 +
and natural number  $  n > 0 $,
 +
there is a pointed Eilenberg–MacLane  $  G $-
 +
complex  $  K ( M,n ) $
 +
such that  $  \pi _ {n} ( K ( M,n ) ) = M $
 +
and  $  \pi _ {m} ( K ( M,n ) ) $
 +
vanishes whenever  $  n \neq m $.  
 +
For every  $  G $-
 +
complex  $  X $,
 +
$  H  ^ {n} _ {G} ( X,M ) = [ X,K ( M,n ) ] _ {G} $,
 +
where  $  [ -, - ] _ {G} $
 +
denotes  $  G $-
 +
homotopy classes of  $  G $-
 +
mappings.
  
where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087064.png" /> is the restriction of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087065.png" /> to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087066.png" />. Bredon cohomology for an arbitrary topological group is studied in [[#References|[a4]]] and [[#References|[a5]]]. Singular ordinary equivariant cohomology is defined in [[#References|[a2]]] (the finite case) and in [[#References|[a3]]]. If a coefficient system <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087067.png" /> is a Mackey functor, then the Bredon cohomology <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087068.png" /> can be extended to an ordinary <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087069.png" />-graded cohomology [[#References|[a6]]].
+
If  $  h  ^ {*} _ {G} ( - ) $
 +
is an equivariant cohomology theory defined on the category  $  G $-
 +
CW, then there exists an Atiyah–Hirzebruch-type spectral sequence
 +
 
 +
$$
 +
H  ^ {p} _ {G} ( X,h  ^ {q} ) \rightarrow h ^ {p + q } _ {G} ( X ) ,
 +
$$
 +
 
 +
where $  h  ^ {q} $
 +
is the restriction of $  h  ^ {q} _ {G} ( - ) $
 +
to $  O _ {G} $.  
 +
Bredon cohomology for an arbitrary topological group is studied in [[#References|[a4]]] and [[#References|[a5]]]. Singular ordinary equivariant cohomology is defined in [[#References|[a2]]] (the finite case) and in [[#References|[a3]]]. If a coefficient system $  M $
 +
is a Mackey functor, then the Bredon cohomology $  H  ^ {*} _ {G} ( -,M ) $
 +
can be extended to an ordinary $  { \mathop{\rm RO} } ( G ) $-
 +
graded cohomology [[#References|[a6]]].
  
 
====References====
 
====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  G.E. Bredon,  "Equivariant cohomology theories" , ''Lecture Notes in Mathematics'' , '''34''' , Springer  (1967)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  T. Bröcker,  "Singuläre Definition der äquivarianten Bredon Homologie"  ''Manuscr. Math.'' , '''5'''  (1971)  pp. 91–102</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  S. Illman,  "Equivariant singular homology and cohomology" , ''Memoirs'' , '''156''' , Amer. Math. Soc.  (1975)</TD></TR><TR><TD valign="top">[a4]</TD> <TD valign="top">  T. Matumoto,  "Equivariant cohomology theories on <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087070.png" />-CW-complexes"  ''Osaka J. Math.'' , '''10'''  (1973)  pp. 51–68</TD></TR><TR><TD valign="top">[a5]</TD> <TD valign="top">  S.J. Wilson,  "Equivariant homology theories on <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/b/b110/b110870/b11087071.png" />-complexes"  ''Trans. Amer. Math. Soc.'' , '''212'''  (1975)  pp. 155–171</TD></TR><TR><TD valign="top">[a6]</TD> <TD valign="top">  L.G. Lewis,  J.P. May,  J. McClure,  "Ordinary RO(G)-graded cohomology"  ''Bull. Amer. Math. Soc.'' , '''4'''  (1981)  pp. 208–212</TD></TR></table>
+
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  G.E. Bredon,  "Equivariant cohomology theories" , ''Lecture Notes in Mathematics'' , '''34''' , Springer  (1967)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  T. Bröcker,  "Singuläre Definition der äquivarianten Bredon Homologie"  ''Manuscr. Math.'' , '''5'''  (1971)  pp. 91–102</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  S. Illman,  "Equivariant singular homology and cohomology" , ''Memoirs'' , '''156''' , Amer. Math. Soc.  (1975)</TD></TR>
 +
<TR><TD valign="top">[a4]</TD> <TD valign="top">  T. Matumoto,  "Equivariant cohomology theories on G-CW-complexes"  ''Osaka J. Math.'' , '''10'''  (1973)  pp. 51–68</TD></TR><TR><TD valign="top">[a5]</TD> <TD valign="top">  S.J. Wilson,  "Equivariant homology theories on G-complexes"  ''Trans. Amer. Math. Soc.'' , '''212'''  (1975)  pp. 155–171</TD></TR><TR><TD valign="top">[a6]</TD> <TD valign="top">  L.G. Lewis,  J.P. May,  J. McClure,  "Ordinary RO(G)-graded cohomology"  ''Bull. Amer. Math. Soc.'' , '''4'''  (1981)  pp. 208–212</TD></TR></table>

Latest revision as of 08:45, 26 March 2023


An ordinary equivariant cohomology for a finite group $ G $, defined in [a1], on the category $ G $- CW of $ G $- complexes (cf. Complex; CW-complex). The objects of $ G $- CW are the CW-complexes $ X $ with a cellular action of $ G $, satisfying the condition that, for every subgroup $ H $ of $ G $, the fixed point set $ X ^ {H} $ is a subcomplex of $ X $. The morphisms are the cellular $ G $- mappings. Let $ O _ {G} $ be the full subcategory of $ G $- CW whose objects are the $ G $- orbits $ G/H $, where $ H $ is a subgroup of $ G $. For every contravariant functor $ M $ from $ O _ {G} $ to the category $ { \mathop{\rm Ab} } $ of Abelian groups, there exists a Bredon cohomology theory $ \{ H ^ {n} _ {G} ( -,M ) \} _ {n \in \mathbf N } $ which, after restriction to $ O _ {G} $, vanishes for $ n > 0 $ and is equal to $ M $ for $ n = 0 $.

Let $ c _ {*} ( X ) $ be the chain complex of functors from $ O _ {G} $ to $ { \mathop{\rm Ab} } $ such that, for every subgroup $ H $ of $ G $, $ c _ {*} ( X ) ( G/H ) = C _ {*} ( X ^ {H} ) $ is the ordinary cellular chain complex of $ X ^ {H} $. Then

$$ H ^ {n} _ {G} ( X,M ) = H ^ {n} ( { \mathop{\rm Hom} } _ {O _ {G} } ( c _ {*} ( X ) ,M ) ) , $$

where $ { \mathop{\rm Hom} } _ {O _ {G} } ( -, - ) $ denotes the set of natural transformations of functors. The functors $ c _ {n} ( X ) $ are projective objects in the category of coefficient systems and there is a spectral sequence

$$ { \mathop{\rm Ext} } ^ {p} _ {O _ {G} } ( h _ {q} ( X ) ,M ) \Rightarrow H ^ {p + q } _ {G} ( X,M ) , $$

where $ h _ {q} ( X ) ( G/H ) = H _ {q} ( X ^ {H} ) $.

Let $ Y $ be a $ G $- space with base point $ y _ {0} $( cf., e.g., Equivariant cohomology). Important examples of coefficient systems are the homotopy group functors $ \pi _ {n} ( Y ) $ defined by $ \pi _ {n} ( Y ) ( G/H ) = \pi _ {n} ( Y ^ {H} ,y _ {0} ) $. The obstruction theory for $ G $- mappings $ f : X \rightarrow Y $ is formulated in terms of the cohomology groups $ H ^ {n} _ {G} ( X, \pi _ {m} ( Y ) ) $. For any coefficient system $ M $ and natural number $ n > 0 $, there is a pointed Eilenberg–MacLane $ G $- complex $ K ( M,n ) $ such that $ \pi _ {n} ( K ( M,n ) ) = M $ and $ \pi _ {m} ( K ( M,n ) ) $ vanishes whenever $ n \neq m $. For every $ G $- complex $ X $, $ H ^ {n} _ {G} ( X,M ) = [ X,K ( M,n ) ] _ {G} $, where $ [ -, - ] _ {G} $ denotes $ G $- homotopy classes of $ G $- mappings.

If $ h ^ {*} _ {G} ( - ) $ is an equivariant cohomology theory defined on the category $ G $- CW, then there exists an Atiyah–Hirzebruch-type spectral sequence

$$ H ^ {p} _ {G} ( X,h ^ {q} ) \rightarrow h ^ {p + q } _ {G} ( X ) , $$

where $ h ^ {q} $ is the restriction of $ h ^ {q} _ {G} ( - ) $ to $ O _ {G} $. Bredon cohomology for an arbitrary topological group is studied in [a4] and [a5]. Singular ordinary equivariant cohomology is defined in [a2] (the finite case) and in [a3]. If a coefficient system $ M $ is a Mackey functor, then the Bredon cohomology $ H ^ {*} _ {G} ( -,M ) $ can be extended to an ordinary $ { \mathop{\rm RO} } ( G ) $- graded cohomology [a6].

References

[a1] G.E. Bredon, "Equivariant cohomology theories" , Lecture Notes in Mathematics , 34 , Springer (1967)
[a2] T. Bröcker, "Singuläre Definition der äquivarianten Bredon Homologie" Manuscr. Math. , 5 (1971) pp. 91–102
[a3] S. Illman, "Equivariant singular homology and cohomology" , Memoirs , 156 , Amer. Math. Soc. (1975)
[a4] T. Matumoto, "Equivariant cohomology theories on G-CW-complexes" Osaka J. Math. , 10 (1973) pp. 51–68
[a5] S.J. Wilson, "Equivariant homology theories on G-complexes" Trans. Amer. Math. Soc. , 212 (1975) pp. 155–171
[a6] L.G. Lewis, J.P. May, J. McClure, "Ordinary RO(G)-graded cohomology" Bull. Amer. Math. Soc. , 4 (1981) pp. 208–212
How to Cite This Entry:
Bredon cohomology. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bredon_cohomology&oldid=16015
This article was adapted from an original article by J. Słomińska (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article