4
votes
1answer
164 views

Link for “A spine for Teichmüller space”, preprint by Thurston

Can someone please give any link or mention any source where I can find the following preprint. W.Thurston, A spine for Teichmüller space, preprint, three pages, 1986.
0
votes
1answer
141 views

Torelli group of a punctured elliptic curve

Let $T_{g,n}$ be the Torelli group of a $n$-punctured surface $S=\overline{S}\setminus\{x_1,\ldots,x_n\}$, with $\overline S$ orientable, closed and of genus $g$. By definition, $T_{g,n}$ is the ...
2
votes
0answers
37 views

Explicit local expression for Bers embedding in genus 2

Let $\mathcal T_{g,n}$ be the Teichmüller space of genus g compact Riemann surfaces with $n$ marked points. According to Riemann, this is a complex manifold of complex dimension 3g-3+n. Bers ...
1
vote
1answer
209 views

References for Teichmüller space of pointed elliptic curves

Where can I find an elementary introduction (construction, description, main properties) to the Teichmüller space ${\cal T}_{1,n}$ of elliptic curves with $n$-marked points? Same question for the ...
10
votes
4answers
878 views

Analytic function avoiding elements of the modular group

A friend recently told me the following two facts, for which he cannot recall a proof or a reference (but he remembers seeing them in the literature): Let $f$ be a holomorphic function mapping the ...
11
votes
7answers
1k views

What are some Applications of Teichmüller Theory?

I'm trying to collect some specific examples of applications of Teichmüller Theory. Here are some things I have collected thus far: No-wandering-domain Theorem (Sullivan) Theorems of Thurston ...
3
votes
1answer
268 views

Strata of quadratic differentials from rational billiards

Given a quadratic differential $q$ on a surface of genus $g$, we say that $q\in \mathcal Q(k_1,\ldots,k_n)$ if $q$ has $n$ distinct zeroes of order $k_1,\ldots,k_n$ respectively. The set $\mathcal ...
0
votes
0answers
153 views

Quick references/sources for the hyperbolic Riemann Surfaces with boundary

Hello, Here I am asking for a reference for the universal cover of hyperbolic Riemann surfaces with geodesic boundaries. For example, I want to know how the universal cover/fundamental domain of ...
3
votes
0answers
362 views

Boundary regularity of the solution to the Beltrami equation

Hello, this question might sound a little vague, but I still dare to state , and I am basically requesting for some reference: Let us consider the orientation-preserving homeomorphic solutions $f: D ...