The multiplicativity of fixed point invariants

Ponto, Kate¹ ; Shulman, Michael²

¹Department of Mathematics, University of Kentucky, 719 Patterson Office Tower, Lexington, KY 40506, USA
²Department of Mathematics and Computer Science, University of San Diego, Serra Hall 133, 5998 Alcalá Park, San Diego, CA 92110, USA

Algebraic and Geometric Topology, Tome 14 (2014) no. 3, pp. 1275-1306

Résumé

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.

Détail

DOI : 10.2140/agt.2014.14.1275

Classification : 55M20, 18D05, 55R05
Keywords: Lefschetz number, Reidemeister trace, Nielsen number, trace

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