#### Volume 17, issue 4 (2017)

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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 $THH\left(DX\right)$ and the free loop space ${\Sigma }_{+}^{\infty }LX$ is in fact a genuinely ${S}^{1}$–equivariant duality that preserves the ${C}_{n}$–fixed points. Our proof uses an elementary but surprisingly useful rigidity theorem for the geometric fixed point functor ${\Phi }^{G}$ 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
##### Publication
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/