arxiv: 1711.11404 · v2 · pith:XNFAXE3Hnew · submitted 2017-11-30 · 🧮 math.GT · math.AT· math.DG

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

Mauricio Bustamante , Francis Thomas Farrell , Yi Jiang This is my paper

classification 🧮 math.GT math.ATmath.DG

keywords curvednegativelybundleshyperbolicmetricssomediffelements

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

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