Geodesic
The Teichmüller space of pinched negatively curved metrics on a hyperbolic manifold is not contractible
F. Thomas Farrell1 ; Pedro Ontaneda1
1 Department of Mathematical Sciences<br/>Binghamton University<br/>Binghamton, NY 13902-6000<br/>United States
Annals of mathematics, Tome 170 (2009) no. 1, pp. 45-65.

Voir la notice de l'article provenant de la source Annals of Mathematics website

For a smooth manifold $M$ we define the Teichmüller space $\mathcal{T}(M)$ of all Riemannian metrics on $M$ and the Teichmüller space $\mathcal{T}^\epsilon(M)$ of $\epsilon$-pinched negatively curved metrics on $M$, where $0\leq\epsilon\leq\infty$. We prove that if $M$ is hyperbolic, the natural inclusion $\mathcal{T}^\epsilon(M)\hookrightarrow\mathcal{T}(M)$ is, in general, not homotopically trivial. In particular, $\mathcal{T}^\epsilon(M)$ is, in general, not contractible.
DOI : 10.4007/annals.2009.170.45

F. Thomas Farrell 1 ; Pedro Ontaneda 1

1 Department of Mathematical Sciences<br/>Binghamton University<br/>Binghamton, NY 13902-6000<br/>United States 
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     title = {The {Teichm\"uller} space of pinched negatively curved metrics on a hyperbolic manifold is not contractible},
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F. Thomas Farrell; Pedro Ontaneda. The Teichmüller space of pinched negatively curved metrics on a hyperbolic manifold is not contractible. Annals of mathematics, Tome 170 (2009) no. 1, pp. 45-65. doi : 10.4007/annals.2009.170.45. http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.45/

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