THE THOM ISOMORPHISM FOR NONORIENTABLE BUNDLES

摘要

The classical theory of Thorn isomorphisms is extended to nonorientable vector bundles. The properties of orientation sheaves of bundles and of the Thorn and Euler classes τ 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 τ and e is confirmed. It is shown that the Thorn isomorphisms, together with their form, are consequences of the Poincare duality.