Twisted Lefschetz number and Nielsen number

Abstract

We study the twisted Lefschetz number, which is a generalization of classical Lefschetz number. A formula in terms of homology with local coefficients is given. We then propose a method to estimate the Nielsen number. As applications, an algorithm for computing the Nielsen number of a self map of a space with abelian fundamental group is discussed; and Bass' conjecture for a class of groups is proved.