Algebraic & Geometric Topology

Relative fixed point theory

Kate Ponto

Full-text: Open access

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.

Article information

Source
Algebr. Geom. Topol., Volume 11, Number 2 (2011), 839-886.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715211

Digital Object Identifier
doi:10.2140/agt.2011.11.839

Mathematical Reviews number (MathSciNet)
MR2782545

Zentralblatt MATH identifier
1218.55001

Subjects
Primary: 55M20: Fixed points and coincidences [See also 54H25]
Secondary: 18D05: Double categories, 2-categories, bicategories and generalizations 55P25: Spanier-Whitehead duality

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

Citation

Ponto, Kate. Relative fixed point theory. Algebr. Geom. Topol. 11 (2011), no. 2, 839--886. doi:10.2140/agt.2011.11.839. https://projecteuclid.org/euclid.agt/1513715211


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