Talk:Equivariant cohomology

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Why is this page in the symplectic topology category? Dave Rosoff 22:40, 25 April 2006 (UTC)

Never mind. (That was silly of me.) Dave Rosoff 00:07, 24 May 2006 (UTC)

this really isnt the right way to do any equivariant anything. This is a somewhat feasible construction, but it is not clean per se. What you do is the classical thing, you construct your cohomology or homology theory in some equivariant category. let G be a some suitably nice group, take the category of G-CW-complexes and G-maps (note that you need the group action to be cellular or "suitably nice"). in fact this is what you really ought to expect for some sort of equivariant cohomology theory. The construction that is up is really ad hoc and not reflective of the standard nature of homotopy theory. see Bredon's springer lecture notes in mathematics for more details. The only reason i know this is that i asked my advisor about equivariant theory in general and i mentioned the construction from wikipedia and he responded that this is not the way to think of it. and he is right!

The right way to think about it is really dependent on what you are using it for. I prefer the "twisted de Rham operator" view for my research, you prefer the G-CW-complexes view, and other people prefer the view here. Right way or not, this is the way it is introduced in most textbooks/lecture notes. Bredon is mostly talking about finite groups anyway in this lecture notes.131.211.241.54 (talk) 13:34, 9 May 2008 (UTC)