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Results tagged with gr.group-theory
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user 25511
Questions about the branch of algebra that deals with groups.
14
votes
3
answers
679
views
Compact manifolds with big mapping class group
I was wondering if compact surfaces were the only compact manifolds with a "big" or "complicated" mapping class group.
Are there higher dimensional manifolds (which are not in some way reducible to …
- 2,696
9
votes
1
answer
1k
views
Fundamental group of an hyperbolic $4$-manifold
Good afternoon everyone,
I have a very general question about hyperbolic manifolds and their fundamental groups in high dimension (at least $4$). If the theory of surfaces and $3$-manifolds provide …
- 2,696
6
votes
3
answers
607
views
Action of $\pi_1(S)$ on its commutator subgroup
Let $G$ be a group. It acts canonically on its derived subgroup by conjugation. Can on describe the orbits of this action when $G$ is the fundamental group of a compact orientable surface of genus $g …
- 2,696
1
vote
1
answer
432
views
Find a simple closed curve in $S$ which represents a commutator in $\pi_1 S$
I am interested in the following problem : decide if a certain element of the fundamental group can be represented by a simple closed curve. The general case has already been asked and answered on MO …
- 2,696