Topological obstructions to fatness

Florit, Luis A¹ ; Ziller, Wolfgang²

¹ IMPA, Estrada Dona Castorina, 110, 22460-320 Rio de Janeiro, Brazil
² Department of Mathematics, University of Pennsylvania, 3451 Walnut Street, Philadelphia PA 19104, USA

Geometry & topology, Tome 15 (2011) no. 2, pp. 891-925.

Résumé

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.

Détail

DOI : 10.2140/gt.2011.15.891

Keywords: positive curvature, submersion, fat principle bundle

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