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Register a new userTopological Hochschild Homology of H(Z/p^k)
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Authors
Nitu Kitchloo
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In this short note we study the topological Hoschschild homology of Eilenberg-MacLane spectra for finite cyclic groups. In particular, we show that the Eilenberg-MacLane spectrum H(Z/p^k) is a Thom spectrum for any prime p (except, possibly, when p=k=2) and we also compute its topological Hoschshild homology. This yields a short proof of the results obtained by Brun, and by Pirashvili except for the anomalous case p=k=2.
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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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