Algebraic & Geometric Topology

The multiplicativity of fixed point invariants

Kate Ponto and Michael Shulman

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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.

Article information

Algebr. Geom. Topol., Volume 14, Number 3 (2014), 1275-1306.

Received: 5 January 2013
Revised: 27 October 2013
Accepted: 28 October 2013
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55M20: Fixed points and coincidences [See also 54H25]
Secondary: 18D05: Double categories, 2-categories, bicategories and generalizations 55R05: Fiber spaces

Lefschetz number Reidemeister trace Nielsen number trace


Ponto, Kate; Shulman, Michael. The multiplicativity of fixed point invariants. Algebr. Geom. Topol. 14 (2014), no. 3, 1275--1306. doi:10.2140/agt.2014.14.1275.

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