Abstract
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.

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@techreport{1,
author = {Farrell, F. T. and Ontaneda, P.},
title = {On the topology of the space of negatively curved metrics},
type = {preprint},
arxiv = {math/0607367},
year = {2006},
} 
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@techreport{2,
author = {Farrell, F. T. and Ontaneda, P.},
title = {Teichmüller spaces and bundles with negatively curved fibers},
type = {preprint},
arxiv = {0709.0998},
year = {2007},
} 
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@techreport{3,
author = {Farrell, F. T. and Ontaneda, P.},
title = {The moduli space of negatively curved metrics of a hyperbolic manifold},
type = {preprint},
url = {http://arxiv.org/abs/0805.2635},
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year = {2008},
} 
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ISSN = {00029947},
CODEN = {TAMTAM},
MRCLASS = {58E11 (53C25 58G11)},
MRNUMBER = {93j:58029},
ZBLNUMBER = {0804.53054},
MRREVIEWER = {Yi Bing Shen},
DOI = {10.2307/2154433},
}