Hodge-theoretic Atiyah-Meyer formulae and the stratified multiplicative property

Abstract

In this note we survey Hodge-theoretic formulae of Atiyah-Meyer type for genera and characteristic classes of complex algebraic varieties, and derive some new and interesting applications. We also present various extensions to the singular setting of the Chern-Hirzebruch-Serre signature formula.

Revised version to be published in the Proceedings of the School and Workshop on the Geometry and Topology of Singularities (L^e Fest). Few typos corrected and some cosmetic changes