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

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 Lclasses. 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 Q to the Q-homology functor H ( ; Q) satisfying a certain normalization condition, just like MacPherson's Chern classes and Baum-Fulton-MacPherson's Todd classes.