Fixed Point Theory and Applications 
Volume 2006 (2006), Article ID 34143, 20 pages
doi:10.1155/FPTA/2006/34143

A base-point-free definition of the Lefschetz invariant

Vesta Coufal

 Department of Mathematics, Fort Lewis College, Durango 81301, CO, USA
Received 30 November 2004; Accepted 21 July 2005

Abstract

In classical Lefschetz-Nielsen theory, one defines the Lefschetz invariant L(f) of an endomorphism f of a manifold M. The definition depends on the fundamental group of M, and hence on choosing a base point ∗∈M and a base path from ∗ to f(∗). At times, it is inconvenient or impossible to make these choices. In this paper, we use the fundamental groupoid to define a base-point-free version of the Lefschetz invariant.