Negatively curved bundles in the Igusa stable range
Accepted version
Peer-reviewed
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Repository DOI
Change log
Authors
Bustamante, Mauricio
Farrell, Francis Thomas
Jiang, Yi
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.
Description
Keywords
58D17 (primary), 57R10 (secondary)
Journal Title
Journal of Topology
Conference Name
Journal ISSN
1753-8416
1753-8424
1753-8424
Volume Title
13
Publisher
Wiley-Blackwell
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All rights reserved
Sponsorship
The first author is supported by the DFG Priority Programme Geometry at Infinity (SPP 2026): Spaces and moduli spaces of Riemannian metrics with curvature bounds on compact and non‐compact manifolds. The third author is partially supported by the grant NSFC 11571343.