1
vote
1answer
119 views

Is the equivariant Gysin map an $H_G^*(\text{pt})$-module morphism?

Let $G$ be a complex reductive group, $X$ a smooth projective variety on which $G$ acts algebraically, and $Y \subseteq X$ a $G$-invariant smooth closed subvariety such that $X\setminus Y$ is also ...
11
votes
2answers
443 views

Microlocalizing Hochschild homology

A recent paper of Ben-Zvi and Nadler gives a general formalism for understanding "dimensions" in sheaf theories. Without getting too far into details, amongst other things, this formalism allows us ...
1
vote
0answers
114 views

When is equivariant cohomology generated by equivariant Euler classes?

Let $X$ be a smooth complex projective variety acted upon by algebraically by a complex torus $T$. Let $F_1,\ldots,F_n$ be the connected components of $X^T$ and assume that the restriction map ...
7
votes
2answers
398 views

Equivariant Stratifications of a Variety

Let $X$ be a complex variety acted upon algebraically by a complex torus $T$. Suppose that $\{X_{\beta}\}_{\beta\in S}$ is a finite $T$-equivariant stratification of $X$, so that the $X_{\beta}$ are ...
3
votes
1answer
187 views

$GL_k$-equivariant cohomology of $k\times n$ matrices

I'm having a surprisingly hard time finding references for some facts about $GL_k$-equivariant cohomology of the space of $k\times n$ matrices. Specifically, I believe the following things to be true: ...
2
votes
0answers
91 views

Equivariant Cohomology of Non-Compact Spaces via Fixed Points

Let $T$ be a complex torus and $X$ a smooth quasi-projective $T$-variety with finitely many fixed points. Denote by $\varphi:H_{T}(X)\rightarrow H_{T}(X^T)$ the map on equivariant cohomology induced ...
0
votes
1answer
262 views

Simple Equivariant homology [no borel-Moore]

Hey. I'm working with Bredon's equivariant cohomology. At some point I need to compute the $4$th equivariant cohomology group of $S^1 \x D^3$ relatively to its boundary for the antipodal action of ...