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Results tagged with teichmuller-theory
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user 7460
3
votes
Defining the natural co-ordinate for a holomorphic quadratic differential near a zero of odd...
The following result can be found in the book of Strebel "Quadratic differentials", p. 29.
Theorem
In the neighborhood of any zero $P_0$ we can introduce a local parameter $\xi$, such that $P_0$ cor …
- 66.3k
3
votes
Accepted
Mapping class group of a punctured genus 0 surface
Let $S_g$ be a compact Riemann surface of genus $g$ with $n$ marked points $x_1, \ldots, x_n$, and set $S_{g, \, n}:=S_g - \{x_0, \ldots, x_n\}$. Also, denote by $\pi_{g, \, n}$ the fundamental group …
- 66.3k
8
votes
Accepted
Universal covering of a 2-sphere without $n$ points
I think this is part of the classical theory of Fuchsian groups.
For instance, in the case $n=3$ the fundamental group of the thrice punctured sphere can be explicitly identified with the congruence …
- 66.3k