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Difference between revisions of "Simple homotopy type"

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Two CW-complexes <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s085/s085230/s0852301.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s085/s085230/s0852302.png" /> are simple homotopy equivalent if there is a homotopy equivalence <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s085/s085230/s0852303.png" /> whose [[Whitehead torsion|Whitehead torsion]] vanishes. An equivalence class under simple homotopy equivalence is called a simple homotopy type.
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Two CW-complexes  $  K $,
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$  L $
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are simple homotopy equivalent if there is a homotopy equivalence $  \tau : K \rightarrow L $
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whose [[Whitehead torsion|Whitehead torsion]] vanishes. An equivalence class under simple homotopy equivalence is called a simple homotopy type.
  
 
====Comments====
 
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====References====
 
====References====
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  G. de Rham,  "Torsion et type simple d'homotopie" , ''Lect. notes in math.'' , '''48''' , Springer  (1967)</TD></TR></table>
 
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  G. de Rham,  "Torsion et type simple d'homotopie" , ''Lect. notes in math.'' , '''48''' , Springer  (1967)</TD></TR></table>

Latest revision as of 08:13, 6 June 2020


Two CW-complexes $ K $, $ L $ are simple homotopy equivalent if there is a homotopy equivalence $ \tau : K \rightarrow L $ whose Whitehead torsion vanishes. An equivalence class under simple homotopy equivalence is called a simple homotopy type.

Comments

References

[a1] G. de Rham, "Torsion et type simple d'homotopie" , Lect. notes in math. , 48 , Springer (1967)
How to Cite This Entry:
Simple homotopy type. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Simple_homotopy_type&oldid=48705
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