Notes by P. Pragacz and Andrzej Weber

Lectures on Characteristic Classes of Constructible Functions

The following lectures were delivered at the Mini-School ''Characteristic classes of singular varieties'' in Banach Center, 22-28 April 2002, by Joerg Schuermann. These lectures discuss the calculus of characteristic classes associated with constructible functions on possibly singular varieties, and focus on the specialization properties. The point of view of characteristic classes of Lagrangian cycles is emphasized. A Verdier-type Riemann-Roch theorem is discussed.

Contents: 1. History. 2. Calculus of constructible functions. 3. Stratified Morse theory for constructible functions and Lagrangian cycles. 4. Characteristic classes of Lagrangian cycles. 5. Verdier-Riemann-Roch theorem and Milnor classes. 6. Appendix: Two letters of J. Schuermann. References.

These notes were prepared by Piotr Pragacz and Andrzej Weber. Their contribution is - apart of some aspects of proofs, mentioned in the text - of purely redactional nature.