Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 34143, 20 pages

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

Copyright © 2006 Vesta Coufal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.