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Journal of Mathematical Sciences

, Volume 136, Issue 5, pp 4166–4200 | Cite as

The Thom isomorphism for nonorientable bundles

  • E. G. Sklyarenko
Article
  • 67 Downloads

Abstract

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 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 Thom isomorphisms, together with their form, are consequences of the Poincaré duality.

Keywords

Manifold Exact Sequence Spectral Sequence Cohomology Class Normal Bundle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • E. G. Sklyarenko
    • 1
  1. 1.Department of Higher Geometry and Topology, Faculty Mechanics and MathematicsMoscow State UniversityMoscowRussia

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