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The multiplicativity of fixed point invariants

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arxiv 1203.0950 v3 pith:6QWJNM6N submitted 2012-03-05 math.AT math.CT

Kate Ponto , Michael Shulman This is my paper · ORCID
classification math.ATmath.CT
keywords theoremsinvariantslefschetzmultiplicativityabstractbicategoricalcontextcontexts
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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.

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  1. Iterated traces in 2-categories and Lefschetz theorems

    math.AT 2019-08 conditional novelty 7.0 of 10

    Iterated traces in any 2-dualizable symmetric monoidal bicategory commute, recovering and extending a wide family of Lefschetz-type theorems.

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