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 Teichm¨uller 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.
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 Teichmuller 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.
