Volume 15, issue 2 (2011)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Topological obstructions to fatness

Luis A Florit and Wolfgang Ziller

Geometry & Topology 15 (2011) 891–925
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