2
votes
1answer
13 views
equivariant orientation
Assume that $G$ is a compact Lie group and $M$ is a smooth oriented manifold on which $G$ acts freely. Then the orbit space $M/G$ is a smooth manifold with dimension $dimM-dimG$. I …
1
vote
1answer
71 views
Braided coverings and braided monodromy
We can map from set of coverings over $X$ to symmetric group $\mathfrak{S}_n$ via monodromy (if we fix a loop at the basepoint). Also we can consider braid group $Br_n(Y)$, allow s …
2
votes
2answers
193 views
Why is the equivariant Euler class a character ?
Let us first precise the question : let $T$ be a torus, $\alpha : T \to \mathbb{C}$ be an irreducible character. I am interested in the $T$-equivariant Euler class of the ($T$-equi …
0
votes
1answer
119 views
Subvarieties with different topology representing the same cycle
Let $X$ be a topological space, and $Y,Z$ be subspaces. My question is a bit vague and open-ended: when is it the case that, if $Y$ and $Z$ represent the same (nonzero) cycle in ho …
2
votes
2answers
241 views
Equivariant Cohomology of a Complex Projective Variety
Suppose that I have a complex projective variety $X$ endowed with an algebraic action of a complex torus $T$. Suppose also that the set $X^T$ of fixed points is finite. I would lik …
14
votes
1answer
761 views
Is Lemma A.1.5.7 in Higher Topos Theory correct?
Hello to everyone,
I am studying the properties of combinatorial model categories, following the exposition given by Jacob Lurie in Higher Topos Theory ([HTT] from now on), in sec …
1
vote
1answer
148 views
equivariant euler class
Let $\pi:E\longrightarrow B$ be a $G-$vector bundle and $s:B\longrightarrow E$ be an equivariant smooth section such that $s^{-1}(0)$ is compact, where $G$ is a compact Lie group. …
6
votes
2answers
273 views
Weights on equivariant cohomology?
Let $X$ be a quasi-projective variety over the complex numbers, equipped with an action of a linear algebraic group $G$.
Is there a natural mixed Hodge structure on its equivaria …
4
votes
1answer
69 views
Fundamental groups of normal complex quasi-projective varieties
I would like to know if there is an explicit example of a finitely presented group that can not be realised as the (topological) fundamental group of a normal complex quasi-project …
4
votes
1answer
153 views
Do we have a “topological assembly map” in the Baum-Connes conjecture?
In the equivariant Atiyah-Singer index theorem, when $G$ is a compact group acting on a manifold $M$ and $R(G)$ is the representation ring of $G$. We have the analytic index
$$
\te …
0
votes
0answers
81 views
equivariant singular homology
Let $M$ be a smooth $G-$manifold, where $G$ is a compact Lie group. From the result of S.Illman that $M$ admits an equivariant triangulation. Moreover, we can construct the equivar …
4
votes
2answers
296 views
Is there an analogous concept for the degree of a map, when the spaces are singular?
Let $M$ and $N$ be two smooth compact, oriented manifolds and
$X\subset M$ an oriented submanifold of $M$ of dimension $k$
(not necessarily closed). Suppose in addition that $\bar …
7
votes
0answers
113 views
Thom isomorphism’s effect on module structure of n-oriented spectra
This question is specifically related to the spectra $X(n)$ used in Devinatz, Hopkins and Smith's proof of the nilpotence conjectures, but any general answer in terms of the Thom i …
0
votes
0answers
50 views
Krull dimension in equivariant cohomology
Let a compact Lie group $G$ act on a manifold $X$. Let $\mathbb Q$ be the field of rational
numbers and assume that cohomology $H^{\ast} (X)$ with $\mathbb Q$-coeffiecients is
fi …
5
votes
2answers
168 views
Action of an isomorphism in cohomology as the intersection with the class of the graph
Let $X$ and $Y$ be two complex manifolds of dimension 2 and let $\varphi:X\rightarrow Y$ be an isomorphism.
I have read that the action of $\varphi^*:H^2(Y,\mathbb{Z})\rightarrow …

