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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 …
Lee Mosher's user avatar
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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 …
Lee Mosher's user avatar
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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 …
Lee Mosher's user avatar
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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 …
Lee Mosher's user avatar
  • 15.4k