...x in the category of $\mathbf{Z}$-modules over $\mathcal{O}_G$. Similarly, equivariant local cohomology can be described using modules over a category depending o
For $RO(G)$-graded equivariant ordinary cohomology one has to replace the orbit category $\mathcal{O}_G$ w
3 KB (473 words) - 18:52, 28 October 2016
$#C+1 = 30 : ~/encyclopedia/old_files/data/E036/E.0306090 Equivariant cohomology
...ogy]] that takes the action of some group into account. More precisely, an equivariant cohomology in the category of $ G $-
5 KB (772 words) - 11:12, 20 January 2021
An ordinary [[Equivariant cohomology|equivariant cohomology]] for a finite group $ G $,
cf., e.g., [[Equivariant cohomology|Equivariant cohomology]]). Important examples of coefficient systems are the [[Homotopy
5 KB (732 words) - 08:45, 26 March 2023
An [[Equivariant estimator|equivariant estimator]] for the shift parameter with respect to a group of real shifts,
if one uses an equivariant estimator $ \widehat \theta = \widehat \theta ( X) $
4 KB (549 words) - 19:05, 17 January 2024
$#C+1 = 21 : ~/encyclopedia/old_files/data/E036/E.0306100 Equivariant estimator
is an equivariant estimator, or that it preserves the structure of the problem of statistical
3 KB (368 words) - 19:37, 5 June 2020
A statistical decision problem is said to be $ G $-equivariant under a group $ G $
etc.) is $ G $-invariant or $ G $-equivariant. Under these conditions, the decision rule $ \delta : \omega \rightarrow
5 KB (735 words) - 07:44, 13 May 2022
...omments to) [[Morse theory|Morse theory]] and [[#References|[a1]]]) and to equivariant Morse functions (cf. [[#References|[a2]]] and [[#References|[a3]]]).
...TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top"> A. Wasserman, "Equivariant differential topology" ''Topology'' , '''8''' (1969) pp. 127–150</TD><
3 KB (502 words) - 08:01, 6 June 2020
is an equivariant mapping. If $ G $
is an equivariant polynomial mapping from $ X $
3 KB (511 words) - 13:16, 7 April 2023
...uivariant" and also what is meant by "E1 and E2 are equivalent" , as $G$-equivariant vector bundles.
...m }$. The equivalence class of this representation depends only on the $G$-equivariant holomorphism class of $E$. If $M$ is a homogeneous $G$-space, this correspo
10 KB (1,550 words) - 16:55, 1 July 2020
equivariant (i.e. is a homomorphism of $ \Gamma $ -
equivariant homomorphisms is an equivalence of these categories.
4 KB (534 words) - 11:05, 17 December 2019
...References|[a2]]], Sect. II.5, and [[#References|[a3]]], Sect. 5.2. For an equivariant version, see [[#References|[a4]]], p. 300ff.
...valign="top">[a4]</td> <td valign="top"> J.P.C. Greenlees, J.P. May, "Equivariant stable homotopy theory" I.M. James (ed.) , ''Handbook of Algebraic Topolog
3 KB (432 words) - 16:46, 1 July 2020
====Equivariant Morse lemma====
...he change of variables $\varphi$ can be taken $G$-invariant. An analogous "equivariant Morse lemma" is true in the real-analytic and the differentiable context. C
5 KB (792 words) - 09:32, 28 June 2014
...^ { h G } = \operatorname { Map } _ { G } ( E _ { G } , X )$, the space of equivariant mappings from the contractible space $E _ { G }$ on which $G$ acts freely t
3 KB (522 words) - 16:57, 1 July 2020
In this case one considers equivariant decision rules $ \delta : X \rightarrow D $(
in the class of equivariant decision rules for every invariant loss function satisfying the following c
5 KB (653 words) - 20:28, 17 January 2024
...the identity mapping $S \rightarrow S$ (cf. also [[Equivariant cohomology|Equivariant cohomology]]), is a [[Homeomorphism|homeomorphism]] of $G \times_{ G _ { x
iv) there is an equivariant mapping $\pi : G ( S ) \rightarrow G ( x )$ that is the identity on $G ( x
11 KB (1,819 words) - 15:30, 1 July 2020
...p of order $r$ in dimension $m$. Several methods for finding $G_m ^ { r }$-equivariant mappings in the $C ^ { \infty }$-case are collected in [[#References|[a1]]]
4 KB (674 words) - 17:02, 1 July 2020
In particular, a morphism is called equivariant if $ \theta _ {b} = \theta $
an equivariant morphism is called a $ G $-
6 KB (847 words) - 20:45, 12 January 2024
...></TR><TR><TD valign="top">[a4]</TD> <TD valign="top"> J.M. Møller, "On equivariant function spaces" ''Pacific J. Math.'' , '''142''' (1990) pp. 103–119</
2 KB (333 words) - 19:38, 5 June 2020
...s for $G/P$: singular (or de Rham) cohomology, the Chow ring, K-theory, or equivariant or quantum versions of these theories. For each, the Schubert cycles form a
3 KB (371 words) - 18:45, 30 March 2012
...ry of simplices; covering spaces, and in particular Cayley graphs; and the equivariant theory. It is also essential for the [[Closed category|closed category]] st
...ry in the sense of D. Quillen, but stronger results in some areas, such as equivariant theory [[#References|[a4]]], can be obtained by constructing the appropriat
13 KB (1,937 words) - 13:10, 24 December 2020