On negatively curved bundles with hyperbolic fibers outside the Igusa stable range

Mauricio Bustamante; Francis Thomas Farrell; Yi Jiang

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arXiv · 1711.11404

On negatively curved bundles with hyperbolic fibers outside the Igusa stable range

Mauricio Bustamante·Francis Thomas Farrell·Yi Jiang

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Abstract

We prove that the Teichm\"{u}ller space $\mathcal{T}^{<0}(M)$ of negatively curved metrics on a hyperbolic manifold $M$ has nontrivial $i$-th rational homotopy groups for some $i> \dim M$. Moreover, some elements of infinite order in $\pi_i B\mbox{Diff}(M)$ can be represented by bundles over $S^i$ with fiberwise negatively curved metrics.

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Mauricio Bustamante, Francis Thomas Farrell, Yi Jiang. 2017-11-30. On negatively curved bundles with hyperbolic fibers outside the Igusa stable range. https://arxiv.org/abs/1711.11404

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