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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Cyclotomic structure in the topological Hochschild homology of $DX$

Cary Malkiewich

Algebraic & Geometric Topology 17 (2017) 2307–2356
Abstract

Let X be a finite CW complex, and let DX be its dual in the category of spectra. We demonstrate that the Poincaré/Koszul duality between THH(DX) and the free loop space Σ+LX is in fact a genuinely S1–equivariant duality that preserves the Cn–fixed points. Our proof uses an elementary but surprisingly useful rigidity theorem for the geometric fixed point functor ΦG of orthogonal G–spectra.

Keywords
topological Hochschild homology, cyclotomic spectra, multiplicative norm, geometric fixed points of orthogonal spectra
Mathematical Subject Classification 2010
Primary: 19D55, 55P43
Secondary: 55P25, 55P91
References
Publication
Received: 17 May 2016
Revised: 21 January 2017
Accepted: 16 February 2017
Published: 3 August 2017
Authors
Cary Malkiewich
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL 61801
United States
http://math.uiuc.edu/~cmalkiew/