arXiv math/04061322004-06math.DGmath.GT

The Teichmüller Space of Pinched Negatively Curved Metrics on a Hyperbolic Manifold is not Contractible

F. T. Farrell, P. Ontaneda

英文摘要：

For a smooth manifold $M$ we define the Teichmüller space $\cT(M)$ of all Riemannian metrics on $M$ and the Teichmüller space $\cT^ε(M)$ of $ε$-pinched negatively curved metrics on $M$, where $0\leqε\leq\infty$. We prove that if $M$ is hyperbolic the natural inclusion $\cT^ε(M)\hookrightarrow\cT(M)$ is, in general, not homotopically trivial. In particular, $\cT^ε(M)$ is, in general, not contractible.

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