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Negatively curved bundles in the Igusa stable range

Accepted version
Peer-reviewed

Type

Article

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

Volume Title

13

Publisher

Wiley-Blackwell

Rights

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.