|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'506'133
Articles rated: 2609
27 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Fenchel-Nielsen coordinates on upper bounded pants decompositions | | Dragomir Šarić
; | | Date: |
26 Sep 2012 | | Abstract: | Let $X_0$ be an infinite genus hyperbolic surface (whose boundary components,
if any, are closed geodesics or punctures) which has an upper bounded pants
decomposition. The length spectrum Teichm"uller space $T_{ls}(X_0)$ consists
of all surfaces $X$ homeomorphic to $X_0$ such that the ratios of the
corresponding simple closed geodesics are uniformly bounded from below and from
above. Alessandrini, Liu, Papadopoulos and Su cite{ALPS} described the
Fenchel-Nielsen coordinates for $T_{ls}(X_0)$ and using these coordinates they
proved that $T_{ls}(X_0)$ is path connected. We use the Fenchel-Nielsen
coordinates for $T_{ls}(X_0)$ to induce a locally biLipschitz homeomorphism
between $l^{infty}$ and $T_{ls}(X_0)$ (which extends analogous results by
Fletcher cite{Fletcher} and by Allessandrini, Liu, Papadopoulos, Su and Sun
cite{ALPSS} for the unreduced and the reduced $T_{qc}(X_0)$). Consequently,
$T_{ls}(X_0)$ is contractible. We also characterize the closure in the length
spectrum metric of the quasiconformal Teichm"uller space $T_{qc}(X_0)$ in
$T_{ls}(X_0)$. | | Source: | arXiv, 1209.5819 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER