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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 (see Astérisque 333, Soc. Math. France, Paris (2010)), topological Hochschild homology and Morita-invariance in bicategorical generality.
Keywords: topological Hochschild homology, Reidemeister trace, Morita equivalence, bicategorical trace
Campbell, Jonathan 1 ; Ponto, Kate 2
@article{10_2140_agt_2019_19_965,
author = {Campbell, Jonathan and Ponto, Kate},
title = {Topological {Hochschild} homology and higher characteristics},
journal = {Algebraic and Geometric Topology},
pages = {965--1017},
publisher = {mathdoc},
volume = {19},
number = {2},
year = {2019},
doi = {10.2140/agt.2019.19.965},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2019.19.965/}
}
TY - JOUR AU - Campbell, Jonathan AU - Ponto, Kate TI - Topological Hochschild homology and higher characteristics JO - Algebraic and Geometric Topology PY - 2019 SP - 965 EP - 1017 VL - 19 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2019.19.965/ DO - 10.2140/agt.2019.19.965 ID - 10_2140_agt_2019_19_965 ER -
%0 Journal Article %A Campbell, Jonathan %A Ponto, Kate %T Topological Hochschild homology and higher characteristics %J Algebraic and Geometric Topology %D 2019 %P 965-1017 %V 19 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2019.19.965/ %R 10.2140/agt.2019.19.965 %F 10_2140_agt_2019_19_965
Campbell, Jonathan; Ponto, Kate. Topological Hochschild homology and higher characteristics. Algebraic and Geometric Topology, Tome 19 (2019) no. 2, pp. 965-1017. doi: 10.2140/agt.2019.19.965
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