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

2017/11/30 by Bustamante, Mauricio, Farrell, Francis Thomas, Jiang, Yi
#Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1711.11404

Abstract

We prove that the Teichmüller space 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 π_i BDiff(M) can be represented by bundles over Sⁱ with fiberwise negatively curved metrics.

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