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Transactions of the American Mathematical Society
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Stiefel-Whitney classes and the conormal cycle of a singular variety

Author(s): Joseph H. G. Fu; 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
Email: fu@math.uga.edu

Clint McCrory
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
Email: clint@math.uga.edu

DOI: 10.1090/S0002-9947-97-01815-1
PII: S 0002-9947(97)01815-1
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 Parusinski for his encouragement and help.
Copyright of article: Copyright 1997, American Mathematical Society




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