FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2003, VOLUME 9, NUMBER 4, PAGES 55-103

The Thom isomorphism for nonorientable bundles

E. G. Sklyarenko

Abstract

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The classical theory of Thom isomorphisms is extended to nonorientable vector bundles. The properties of orientation sheaves of bundles and of the Thom and Euler classes $$t and $e$ with respect to projections, fiber maps, Cartesian products, and Whitney sums of bundles are studied. The validity of standard constructions used in the applications of the classes $$t and $e$ is confirmed. It is shown that the Thom isomorphisms, together with their form, are consequences of the Poincaré duality.

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Last modified: September 24, 2004.