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

Authors: Joseph H. G. Fu and Clint McCrory
Journal: Trans. Amer. Math. Soc. 349 (1997), 809-835
MSC (1991): Primary 14P25, 57R20; Secondary 14P15, 49Q15
MathSciNet review: 1401519
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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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Additional Information

Joseph H. G. Fu
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602

Clint McCrory
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602

Keywords: Stiefel-Whitney class, real analytic set, conormal cycle, characteristic cycle, polar cycle, integral current
Received by editor(s): October 2, 1995
Additional Notes: Research supported in part by NSF grant DMS-9403887. First author also partially supported by NSF grant DMS-9404366. We thank Adam Parusiński for his encouragement and help.
Article copyright: © Copyright 1997 American Mathematical Society

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