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Apr
7 |
comment |
When do colimits agree with homotopy colimits?
Hi Greg, perhaps you mean $X^H$ is contractible for all non-trivial subgroups $H\subset G$ ($G_+$ is cofibrant, but is not contractible for all proper subgroups unless $G$ is trivial). |
Apr
6 |
revised |
$RO(G)$-graded homotopy groups vs. Mackey functors
Expanded argument to clarify dependence on rationals. |
Apr
5 |
comment |
$RO(G)$-graded homotopy groups vs. Mackey functors
@AaronMazel-Gee: Sorry, that was less than clear because I rushed the answer. I filled out the answer a bit more. Hopefully, it is more understandable now. |
Apr
5 |
revised |
$RO(G)$-graded homotopy groups vs. Mackey functors
Added a couple paragraphs of clarifying information and additional information for equivariant $K$-theory. |
Apr
5 |
revised |
$RO(G)$-graded homotopy groups vs. Mackey functors
Added a couple paragraphs of clarifying information and additional information for equivariant $K$-theory. |
Apr
5 |
revised |
$RO(G)$-graded homotopy groups vs. Mackey functors
added 1867 characters in body |
Apr
4 |
revised |
$RO(G)$-graded homotopy groups vs. Mackey functors
Need suspensions to get that C_f is closed under suspension. |
Apr
4 |
revised |
$RO(G)$-graded homotopy groups vs. Mackey functors
deleted 41 characters in body |
Apr
4 |
answered | $RO(G)$-graded homotopy groups vs. Mackey functors |
Aug
27 |
awarded | Yearling |
Feb
23 |
awarded | Nice Question |
Sep
3 |
awarded | Enlightened |
Sep
3 |
awarded | Nice Answer |
Sep
2 |
answered | What is the geometric fixed points of an (equivariant) Eilenberg Maclane Spectrum? |
Aug
27 |
awarded | Yearling |
Aug
20 |
comment |
How does the kernel of the map $\Omega^{\bullet}(X)\rightarrow \Omega^{\bullet}(G\times X)$ relate to equivariant cohomology?
Alternatively one can take the simplicial $G$-space $G^{\cdot+1}$ all of whose face maps are projection maps and whose degeneracies are diagonal maps. You can then take the product of this simplicial $G$-space with the constant simplicial $G$-space $X$. To obtain a simplicial $G$-space which levelwise looks the same as the one in the previous comment, but with different structure maps and different $G$-actions (this one is diagonal and realizes the Borel construction). When $X$ is $G$-free the augmentation admits an extra degeneracy and the the associated cochain complex is exact. |
Aug
20 |
comment |
How does the kernel of the map $\Omega^{\bullet}(X)\rightarrow \Omega^{\bullet}(G\times X)$ relate to equivariant cohomology?
I don't think the projection maps will define a simplicial diagram. For example, if your diagram was simplicial, there should be an equality between the two composite face maps $(g_1,g_2,x)\mapsto g_1 g_2 x$ and $(g_1,g_2,x)\mapsto g_1 x.$ The standard construction uses the group multiplication on $G$ not the projection. Using this construction one obtains an augmented simplicial $G$ space $G^{\cdot+1}\times X\rightarrow X$. This is the bar construction on $X$ and the geometric realization is $G$-homeomorphic to the Borel construction. |
Aug
19 |
revised |
RO(G) grading of Mackey functors
added the keyword rational |
Aug
19 |
revised |
RO(G) grading of Mackey functors
added 41 characters in body |
Aug
19 |
answered | RO(G) grading of Mackey functors |