Stiefel-Whitney classes and the conormal cycle of a singular variety

Fu, Joseph; McCrory, Clint

doi:10.1090/S0002-9947-97-01815-1

Stiefel-Whitney classes and the conormal cycle of a singular variety
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by Joseph H. G. Fu and Clint McCrory PDF

Trans. Amer. Math. Soc. 349 (1997), 809-835 Request permission

Abstract:

A geometric construction of Sullivan’s Stiefel-Whitney homology classes of a real analytic variety $X$ is given by means of the conormal cycle of an embedding of $X$ in a smooth variety. We prove that the Stiefel-Whitney classes define additive natural transformations from certain constructible functions to homology. We also show that, for a complex analytic variety, these classes are the mod 2 reductions of the Chern-MacPherson classes.

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