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Fundam. Prikl. Mat., 2003, Volume 9, Issue 4, Pages 55–103 (Mi fpm750)  

The Thom isomorphism for nonorientable bundles

E. G. Sklyarenko

M. V. Lomonosov Moscow State University

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 $\tau$ 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 $\tau$ 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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English version:
Journal of Mathematical Sciences (New York), 2006, 136:5, 4166–4200

Bibliographic databases:

UDC: 515.145.25

Citation: E. G. Sklyarenko, “The Thom isomorphism for nonorientable bundles”, Fundam. Prikl. Mat., 9:4 (2003), 55–103; J. Math. Sci., 136:5 (2006), 4166–4200

Citation in format AMSBIB
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\by E.~G.~Sklyarenko
\paper The Thom isomorphism for nonorientable bundles
\jour Fundam. Prikl. Mat.
\yr 2003
\vol 9
\issue 4
\pages 55--103
\mathnet{http://mi.mathnet.ru/fpm750}
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\zmath{https://zbmath.org/?q=an:1073.55009}
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\transl
\jour J. Math. Sci.
\yr 2006
\vol 136
\issue 5
\pages 4166--4200
\crossref{https://doi.org/10.1007/s10958-006-0226-3}
\elib{http://elibrary.ru/item.asp?id=13517186}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33745674328}


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  • Фундаментальная и прикладная математика
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