Topological obstructions to fatness

Florit, Luis A; Ziller, Wolfgang

doi:10.2140/gt.2011.15.891

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Topological obstructions to fatness

Luis A Florit and Wolfgang Ziller

Geometry & Topology 15 (2011) 891–925

DOI: 10.2140/gt.2011.15.891

Abstract

Alan Weinstein showed that certain characteristic numbers of any Riemannian submersion with totally geodesic fibers and positive vertizontal curvatures are nonzero. In this paper we explicitly compute these invariants in terms of Chern and Pontrjagin numbers of the bundle. This allows us to show that many bundles do not admit such metrics.

Keywords

positive curvature, submersion, fat principle bundle

Mathematical Subject Classification 2000

Primary: 53C20, 57R20, 57R22

References

Publication

Received: 19 February 2010

Accepted: 20 April 2011

Published: 13 June 2011

Proposed: Tobias H Colding

Seconded: Peter Teichner, Leonid Polterovich

Authors

Luis A Florit
IMPA Estrada Dona Castorina, 110 22460-320 Rio de Janeiro Brazil
http://luis.impa.br
Wolfgang Ziller
Department of Mathematics University of Pennsylvania 3451 Walnut Street Philadelphia PA 19104 USA

Volume 15, issue 2 (2011)