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Results tagged with gr.group-theory
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user 5010
Questions about the branch of algebra that deals with groups.
21
votes
2
answers
683
views
Gluing hexagons to get a locally CAT(0) space
I believe that there are four ways to glue (all) the edges of a regular Euclidean hexagon to get a locally CAT(0) space:
The first two give the torus and the Klein bottle, respectively. What are the …
- 10.1k
8
votes
Accepted
Residual Finiteness of Fundamental Group of Compact 3-Manifold
For the first question, the answer is yes. Geometrization implies that the only non-Haken manifolds irreducible manifolds are compact hyperbolic manifolds (with no cusps), and there again $\pi_1$ is …
- 10.1k
5
votes
Accepted
For a representation V of a finite group G, when is Hom(W, W⊗V) trivial for all irreps W?
One necessary condition is that the center of $G$ needs to act trivially in $V$ for $\mathrm{Hom}(W, W \otimes V)$ to ever be non-trivial. The character of the center justs multiplies in a tensor pro …
- 10.1k
4
votes
2
answers
545
views
Fundamental domain for symmetric group $S_n$ acting on $\mathop{Gr}(k,n)$?
Is there a nice fundamental domain for the symmetric group $S_n$ acting on the Grassmannian of $k$-planes in $\mathbb{R}^n$? (The action of $S_n$ is by permuting the coordinates, of course.)
I'm loo …
- 10.1k