Open Access
2011 Relative fixed point theory
Kate Ponto
Algebr. Geom. Topol. 11(2): 839-886 (2011). DOI: 10.2140/agt.2011.11.839


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.


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Kate Ponto. "Relative fixed point theory." Algebr. Geom. Topol. 11 (2) 839 - 886, 2011.


Received: 1 November 2009; Revised: 2 December 2010; Accepted: 12 December 2010; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1218.55001
MathSciNet: MR2782545
Digital Object Identifier: 10.2140/agt.2011.11.839

Primary: ‎55M20
Secondary: 18D05 , 55P25

Keywords: Bicategory , fixed point , fixed point index , Lefschetz number , Nielsen theory , Reidemeister trace , Trace

Rights: Copyright © 2011 Mathematical Sciences Publishers

Vol.11 • No. 2 • 2011
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