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Index Classes for Vector Fields and their Relation to Certain Characteristic Classes

Oskar Hamlet

Abstract


While studying vector fields on manifolds with boundary there are three important indexes to consider. We construct three cohomology classes to compute these. We relate these classes to other classes, the relative Euler class as defined by Sharafutdinov and the secondary Chern-Euler class as defined by Sha. Our results also yield a new proof of the Poincaré-Hopf index theorem.

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DOI: http://dx.doi.org/10.7146/math.scand.a-15241

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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