Negatively curved bundles in the Igusa stable range
arXiv:1711.11315 · doi:10.1112/topo.12130
Abstract
We use classical results in smoothing theory to extract information about the rational homotopy groups of the space of negatively curved metrics on a high dimensional manifold. It is also shown that smooth M-bundles over spheres equipped with fiberwise negatively curved metrics, represent elements of finite order in the homotopy groups of the classifying space for smooth M-bundles, provided the dimension of M is large enough.
11 pages. v2 one equation added on last page. v3 Appendix with proofs of two technical lemmas added. Also a new corollary about CAT(-1) metrics