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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On Cappell-Shaneson's homology $ L$-classes of singular algebraic varieties


Author: Shoji Yokura
Journal: Trans. Amer. Math. Soc. 347 (1995), 1005-1012
MSC: Primary 57R20; Secondary 14C40, 14F99, 18E30
MathSciNet review: 1283567
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Abstract: S. Cappell and J. Shaneson (Stratifiable maps and topological invariants, J. Amer. Math. Soc. 4 (1991), 521-551) have recently developed a theory of homology $ L$-classes, extending Goresky-MacPherson's homology $ L$-classes. In this paper we show that Cappell-Shaneson's homology $ L$-classes for compact complex, possibly singular, algebraic varieties can be interpreted as a unique natural transformation from a covariant cobordism function $ \Omega $ to the $ {\mathbf{Q}}$-homology functor $ {H_{\ast}}(;{\mathbf{Q}})$ satisfying a certain normalization condition, just like MacPherson's Chern classes and Baum-Fulton-MacPherson's Todd classes.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1283567-6
PII: S 0002-9947(1995)1283567-6
Article copyright: © Copyright 1995 American Mathematical Society