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Topological Hochschild homology and higher characteristics

2019; Mathematical Sciences Publishers; Volume: 19; Issue: 2 Linguagem: Inglês

10.2140/agt.2019.19.965

1472-2747

Jonathan A. Campbell, Kate Ponto,

Advanced Topics in Algebra

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 [Pon10], topological Hochschild homology, and Morita invariance in bicategorical generality.CONTENTS 1. Introduction 1 2. THH for Spectral Categories and Shadows 4 3. Duality and trace 8 4. Morita equivalence in bicategories 14 5. Euler characteristics for base change objects 17 6.Example: Fixed Point Invariants 23 7.A π 0 -level cyclotomic trace 26 Appendix A.