Relative fixed point theory

Ponto, Kate

doi:10.2140/agt.2011.11.839

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Relative fixed point theory

Kate Ponto

Algebraic & Geometric Topology 11 (2011) 839–886

DOI: 10.2140/agt.2011.11.839

Abstract

The Lefschetz fixed point theorem and its converse have many generalizations. One of these generalizations is to endomorphisms of a space relative to a fixed subspace. In this paper we define relative Lefschetz numbers and Reidemeister traces using traces in bicategories with shadows. We use the functoriality of this trace to identify different forms of these invariants and to prove a relative Lefschetz fixed point theorem and its converse.

Keywords

Reidemeister trace, Nielsen theory, fixed point, Lefschetz number, fixed point index, trace, bicategory

Mathematical Subject Classification 2000

Primary: 55M20

Secondary: 18D05, 55P25

References

Publication

Received: 1 November 2009

Revised: 2 December 2010

Accepted: 12 December 2010

Published: 25 March 2011

Authors

Kate Ponto
Department of Mathematics University of Kentucky 719 Patterson Office Tower Lexington KY 40506 USA
http://www.ms.uky.edu/~kate

Volume 11, issue 2 (2011)