Relative fixed point theory

Ponto, Kate¹

¹Department of Mathematics, University of Kentucky, 719 Patterson Office Tower, Lexington KY 40506, USA

Algebraic and Geometric Topology, Tome 11 (2011) no. 2, pp. 839-886

Résumé

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.

Détail

DOI : 10.2140/agt.2011.11.839

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

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