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Science China Mathematics

, Volume 60, Issue 4, pp 569–580 | Cite as

Teichmüller space of negatively curved metrics on complex hyperbolic manifolds is not contractible

Articles Invited Articles

Abstract

We prove that for all n = 4k − 2 and k ≥ 2 there exists a closed smooth complex hyperbolic manifold M with real dimension n having non-trivial π 1(T <0(M)). T <0(M) denotes the Teichmüller space of all negatively curved Riemannian metrics on M, which is the topological quotient of the space of all negatively curved metrics modulo the space of self-diffeomorphisms of M that are homotopic to the identity

Keywords

space of Riemannian metrics negative curvature complex hyperbolic space 

MSC(2010)

58D27 58D17 53C20 57R19 53C55 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Yau Mathematical Sciences Center and Department of Mathematical SciencesTsinghua UniversityBeijingChina
  2. 2.Department of MathematicsOhio State UniversityColumbusUSA

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