All Questions
Tagged with equivariant-homotopy gr.group-theory
7 questions
14
votes
0
answers
341
views
Is this class of groups already in the literature or specified by standard conditions?
In recent work
Lifting $N_\infty$ operads from conjugacy data on homotopical combinatorics / $N_\infty$ operads in equivariant homotopy theory, collaborators
Scott Balchin, Ethan MacBrough, and I ...
- 141
10
votes
2
answers
337
views
Finitely dominated universal spaces for the family of solvable subgroups
$\DeclareMathOperator\PSL{PSL}\DeclareMathOperator\Sz{Sz}$In short, I am interested in the question which finite groups $G$ admit a finitely dominated universal space with respect to the family of ...
- 231
9
votes
0
answers
434
views
Stable homotopy type of $BG^{\wedge}_p$ in algebraic terms
In the mid 90's, Martino- Priddy proved that given two finite groups $G, H$, the following are equivalent:
$\mathbb{F}_p\mathrm{Inj}(P,G)\cong \mathbb{F}_p\mathrm{Inj}(P,H)$ as $\mathbb{F}_p\mathrm{...
- 795
4
votes
2
answers
1k
views
homotopy invariant and coinvariant
Let $V$ be a chain complex, which is either $Z$ or $Z/2$ graded. A circle action on $V$ is
by definition an action of the dga $H_\ast(S^1)$. This consists of a map $D : V → V$ , which is of square ...
- 113
4
votes
0
answers
100
views
When can the trace on cohomology be computed as the Euler characteristic of fixed points?
In this question all groups are finite, and all spaces are nice (eg, simplicial sets).
Given a $G$ space $X$, which we assume has finitely many nonzero cohomology groups, we can compute the trace of ...
- 1,949
4
votes
0
answers
201
views
Decomposition of fiber product of $G$-sets in $G$-orbits
I have posted an identical question in MSE few days ago, but maybe this site is a better adress to discuss this problem:
Let $G$ be a finite group and $K, H \leq G$ two subgroups. Then
the right ...
- 5,966
0
votes
1
answer
154
views
Question about finite G-sets [closed]
Let G be a finite group with subgroups H and K. Then the set of not necessarily equivariant maps from G/H to G/K is itself a finite G-set under the conjugation action. Is there a good description of ...
