ABSTRACT
In this chapter, we extend the Atiyah-Bott-Lefschetz fixed point theorem to the case of manifolds with conical singularities. The classical theorem (Atiyah and Bott 1967) deals with a geometric endomorphism of an elliptic complex on a smooth closed manifold. It says that if all fixed points of the underlying selfmapping of the manifold are nondegenerate, then the Lefschetz number of the endomorphism is equal to the sum of their contributions. Moreover, these contributions are determined by the restrictions of the mappings comprising the endomorphism to the respective fixed points (and independent of the operators constituting the complex).
