Volume 14, issue 3 (2014)

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The multiplicativity of fixed point invariants

Kate Ponto and Michael Shulman

Algebraic & Geometric Topology 14 (2014) 1275–1306
Abstract

We prove two general factorization theorems for fixed-point invariants of fibrations: one for the Lefschetz number and one for the Reidemeister trace. These theorems imply the familiar multiplicativity results for the Lefschetz and Nielsen numbers of a fibration. Moreover, the proofs of these theorems are essentially formal, taking place in the abstract context of bicategorical traces. This makes generalizations to other contexts straightforward.

Keywords
Lefschetz number, Reidemeister trace, Nielsen number, trace
Mathematical Subject Classification 2010
Primary: 55M20
Secondary: 18D05, 55R05
References
Publication
Received: 5 January 2013
Revised: 27 October 2013
Accepted: 28 October 2013
Published: 7 April 2014
Authors
Kate Ponto
Department of Mathematics
University of Kentucky
719 Patterson Office Tower
Lexington, KY 40506
USA
http://www.ms.uky.edu/~kate
Michael Shulman
Department of Mathematics and Computer Science
University of San Diego
Serra Hall 133
5998 Alcalá Park
San Diego, CA 92110
USA
http://home.sandiego.edu/~shulman