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

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（4）
• 页码范围: 569-580
• 页数: 12页
• 语种: 英文
• DOI: 10.1007/s11425-016-0351-8

摘要

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 π1(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.