All Questions
5 questions
5
votes
1
answer
248
views
Explicit check of the invariance of the Weil-Petersson form
Using Fenchel-Nielsen coordinates, the Weil-Petersson metric can be written as
$\omega_{WP} = \sum_{i} d\ell_i \wedge d \tau_i,$
where $i$ is an index labelling the curves of a pants decomposition of ...
- 1,435
4
votes
1
answer
213
views
Conformal map between flat and hyperbolic torus with a boundary
I am confused because I can define two very different complex structures on the torus with a puncture/boundary.
For my first construction, I can imagine removing a disk from a flat torus, inheriting ...
- 355
4
votes
1
answer
2k
views
On Thurston's triangulations of sphere
I have two questions from Thurston's paper [1].
In the paper [1], Thurston talks about classifying certain classes of triangulations of the sphere. Here a triangulation of a sphere a Topological ...
- 239
3
votes
1
answer
853
views
Moduli, Teichmüller spaces and mapping class group of a sphere with four punctures
In the complex analytic setting, it is easy to see that the moduli space of a sphere with four punctures is $\mathcal{M}=\mathbb{CP}^1 / { 0,1,\infty }$, since I can use a Moebius transformation to ...
- 1,435
1
vote
0
answers
261
views
Mirzakhani's work and surfaces with marked points on the boundary
Mirzakhani proved identities for the lengths of geodesic curves on Riemann surfaces of genus $g$ and with $n$ boundary components. She used these to provide an integration scheme over the ...
- 1,435