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

Yokura, Shoji

doi:10.1090/S0002-9947-1995-1283567-6

On Cappell-Shaneson’s homology $L$-classes of singular algebraic varieties
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Trans. Amer. Math. Soc. 347 (1995), 1005-1012 Request permission

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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