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Results tagged with fundamental-group
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user 20787
19
votes
Fundamental groups of noncompact surfaces
I just ran across this question, and thought I would give a precise version of the proof Ilya suggested. I believe I learned this proof in Richie Miller's topology course, Michigan State University, 1 …
- 15.4k
9
votes
The fundamental group of a closed surface without classification of surfaces?
I will answer the question of whether this also gives the classification cheaply.
No.
It gives the classification at the expense of proving that every surface group has a free cocompact action on th …
- 15.4k
3
votes
$P^1$ minus k points
One can always find a fundamental domain for $G$ which is an ideal polygon $P \subset \mathbb{H}$ having $2k-2$ vertices at infinity and $2k-2$ sides, so that the sides are written in cyclic order aro …
- 15.4k
1
vote
When is a three-manifold deck transformation group solvable?
You are asking for free actions of finite, nonsolvable groups on $Y$. If you truly don't care that $Y$ is a rational homology sphere, for any finite group $G$ there exists a closed, connected, orienta …
- 15.4k