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March 19, 2019 | 2:00 p.m. - 3:00 p.m.
Category: Seminar
Location: Faculty/Administration #1140 | Map
656 W. Kirby
Detroit, MI 48202
Cost: Free

Speaker: Michael Weiss, Universitaet Muenster

Title: Rational Pontryagin classes of fiber bundles with fiber R^m

Abstract: The Pontryagin classes are characteristic cohomology classes for real vector bundles. Due to their close relationship with the Chern classes of complex vector bundles, they satisfy some vanishing relations, namely, the Pontryagin classes of a vector bundle of fiber dimension m vanish in cohomological dimensions greater than 2m. It is an important fact in geometric topology, emphasized and established by Thom and Novikov, that the Pontryagin classes make sense in *rational* cohomology for fiber bundles with fiber R^m (without fiberwise vector space structures). The question arises whether these extended Pontryagin classes still satisfy the above vanishing relations. The answer turns out to be no.

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