Teichm\"uller space of negatively curved metrics on Complex Hyperbolic Manifolds is not contractible

F. T. Farrell; G. Sorcar

doi:10.1007/s11425-016-0351-8

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arXiv · 1611.03764

Teichm\"uller space of negatively curved metrics on Complex Hyperbolic Manifolds is not contractible

F. T. Farrell·G. Sorcar

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Abstract

In this paper we prove that for all $n=4k-2$, $k\ge2$ there exists a closed smooth complex hyperbolic manifold $M$ with real dimension $n$ having non-trivial $\pi_1(\mathcal{T}^{<0}(M))$. $\mathcal{T}^{<0}(M)$ 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.

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BibTeX RIS

F. T. Farrell, G. Sorcar. 2016-11-11. Teichm\"uller space of negatively curved metrics on Complex Hyperbolic Manifolds is not contractible. https://doi.org/10.1007/s11425-016-0351-8

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