We establish formulae that show how the topological characteristic L-classes of Goresky and MacPherson, as well as the Hodge-theoretic Hirzebruch type characteristic classes defined by Brasselet, Schürmann and Yokura transform under Gysin restrictions associated to normally nonsingular embeddings of singular spaces. We find that both types of classes transform in the same manner. These results suggest a method of normally nonsingular expansions for computing the above characteristic classes. We illustrate this method by computing Goresky-MacPherson L-classes of some singular Schubert varieties.

This work is supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy EXC-2181/1 - 390900948 (the Heidelberg STRUCTURES Excellence Cluster).