Open Access

A base-point-free definition of the Lefschetz invariant

Fixed Point Theory and Applications20062006:34143

DOI: 10.1155/FPTA/2006/34143

Received: 30 November 2004

Accepted: 21 July 2005

Published: 28 February 2006

Abstract

In classical Lefschetz-Nielsen theory, one defines the Lefschetz invariant of an endomorphism of a manifold . The definition depends on the fundamental group of , and hence on choosing a base point and a base path from to . 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.

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Authors’ Affiliations

(1)
Department of Mathematics, Fort Lewis College

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Copyright

© Vesta Coufal. 2006

This article is published under license to BioMed Central Ltd. 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.