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

2004/06/07 by F. T. Farrell, Farrell, F. T., Pedro Ontaneda +1 · 1 citation
Mathematics · #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0406132

openalex publication_date 2004/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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≤ε≤∞. 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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