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Topological Hochschild Homology and Higher Characteristics

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arxiv 1803.01284 v2 pith:3T7GCEJ7 submitted 2018-03-04 math.AT math.CT

Jonathan A. Campbell , Kate Ponto This is my paper · ORCID
classification math.ATmath.CT
keywords hochschildhomologytopologicaltraceclassicalreidemeisterresultarises
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We show that an important classical fixed point invariant, the Reidemeister trace, arises as a topological Hochschild homology transfer. This generalizes a corresponding classical result for the Euler characteristic and is a first step in showing the Reidemeister trace is in the image of the cyclotomic trace. The main result follows from developing the relationship between shadows, topological Hochschild homology, and Morita invariance in bicategorical generality.

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  1. Frobenius and Verschiebung for $K$-theory of endomorphisms

    math.KT 2025-07 conditional novelty 6.0 of 10

    Frobenius and Verschiebung operations are constructed on reduced K-theory of twisted endomorphisms over noncommutative rings, with the expected trace behavior.

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