Topological obstructions to fatness

Details Topological obstructions to fatness Topological obstructions to fatness

2010-01-06

arxiv.org/abs/1001.0967v3

Mathematics

Differential Geometry

32 pages. To appear in Geom. Topol

Scientific paper

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.

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