All Questions
11 questions
2
votes
0
answers
109
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Further directions in representations of surface group into a Lie group
$\DeclareMathOperator\SL{SL}\DeclareMathOperator\PSL{PSL}$I studied the interpretation of Teichmuller space as a representation space for surface groups in $\PSL(2,\mathbb{R})$.
Now I am planning to ...
CommunityBot
- 1
7
votes
3
answers
413
views
Best source for classification of right-angled hyperbolic hexagons
A standard fact that underlies the Fenchel-Nielsen coordinates on Teichmuller space is the fact that for all triples $(a,b,c)$ of positive real numbers, there exists a unique hyperbolic hexagon whose ...
- 18.7k
3
votes
2
answers
420
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Learning roadmap for Lorentzian geometry
I am asked the question in MSE, but did not get an answer. I hope that this question is appropriate for MOF.
I am interested in Hyperbolic Geometry and its significance in low dimensional geometry (...
- 7,817
2
votes
2
answers
313
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References on Riemann surfaces
I have asked the question in MSE, but did not get an answer.
I am asking a soft question here. I am interested in learning about Hyperbolic Geometry. I have read the book named "Fuchsian Groups&...
- 1,594
1
vote
0
answers
42
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Effect of plumbing a surface on the marked length spectrum
First I'll recall the plumbing procedure.
Let $M$ be a noded Riemann surface with nodes $p_1,\dots, p_n$. There is a family of pairwise disjoint neighbourhoods of each node $U_i$ that has coordinates ...
- 445
5
votes
3
answers
295
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Teichmuller space for surface with cone points
Working on my current research problem, Teichmuller spaces for surfaces with cone points have come into play. It's fairly easy to formulate some of the definitions, a few basic results, etc. To be ...
- 91.8k
8
votes
2
answers
631
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Teichmüller space on non-orientable closed surfaces
It is known that any closed orientable surface of genus $g \geq 2$ admits a hyperbolic metric, and the Teichmüller space of such metrics has dimension $6g - 6$. I was wondering if there is a ...
- 63.9k
1
vote
1
answer
266
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Reference for the result that the systol map from Teichmuller space to curve complex is coarsely Lipschitz
Let $\mathcal{T}(S)$ denotes the Teichmuller space of a finite type surface $S$ equipped with Teichmuller metric and $\mathcal{C}(S)$ denotes the curve complex. Define a map $$\phi:\mathcal{T}(S)\...
- 28.2k
1
vote
1
answer
271
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Ratner theorem and dense geodesic planes in hyperbolic manifolds
Suppose we have a closed hyperbolic $3$-manifold $M$. For any $x\in M$ and plane $\pi$ in $T_xM$ we consider $P$ the geodesic plane exp$(\pi)$ originating from $\pi$. For any $p\in \pi$ we consider ...
- 17k
1
vote
2
answers
360
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Does the Teichmüller space of the pair of pants admit a continuous global section?
Let $P$ be a pair of pants, $H(P)$ be the space of smooth hyperbolic Riemannian metrics with geodesic boundary on $P$, and $T(P)$ be the Teichmüller space of $P$ (quotient of $H(P)$ under smooth ...
- 31.2k
0
votes
0
answers
313
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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 ...
- 1,471