# Tag Info

### Cohomology of quotient by free action

This is true even if the group does not act freely. See Proposition 1.1 of my notes here. I deal with simplicial complexes and work over the rationals, but the statement you give can be proved the ...
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Accepted

### "Rotated" version of the Atiyah-Hirzebruch spectral sequence

Good question. I think the answer is yes. The unnamed spectral sequence is usually referred to as the isotropy spectral sequence. For a group $G$ acting on $X$ and an abelian group $A$ of ...
• 33.6k
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• 26k

### Reading list for Equivariant Cohomology

I would like to point out that the term "equivariant cohomology'' is ambiguous. To those unfamiliar with modern algebraic topology, it means Borel cohomology, the cohomology theory that is the ...
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### Deequivariantisation of indecomposable sheaves

Take $X=pt$ and $G=G_m$ and $k$ to have characteristic zero. The equivariant derived category in this case is equivalent to modules for the homology of the circle, ie exterior algebra on a generator ...
• 22.2k
Accepted

### Calculations of cup products in Bredon cohomology

Frankly, there aren't many calculations out there. Most of the work I know of is on the calculation of the $RO(G)$-graded cohomology of a point, of a projective space, or of $B_GO(n)$. Here are some ...
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Suppose $E \to B$ is a principal $G$-bundle with connection $\omega \in \Omega^1(E,\mathfrak{g})$, and corresponding curvature $\Omega \in \Omega^2(E,\mathfrak{g})$. Then $\Omega^*(E)$ is a ...