Negatively curved bundles in the Igusa stable range
Geometric Topology
2019-11-27 v3 Algebraic Topology
Differential Geometry
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.
Keywords
Cite
@article{arxiv.1711.11315,
title = {Negatively curved bundles in the Igusa stable range},
author = {Mauricio Bustamante and Francis Thomas Farrell and Yi Jiang},
journal= {arXiv preprint arXiv:1711.11315},
year = {2019}
}
Comments
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