Algebraic & Geometric Topology

Cyclotomic structure in the topological Hochschild homology of $DX$

Cary Malkiewich

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.

Article information

Source
Algebr. Geom. Topol., Volume 17, Number 4 (2017), 2307-2356.

Dates
Revised: 21 January 2017
Accepted: 16 February 2017
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.agt/1510841444

Digital Object Identifier
doi:10.2140/agt.2017.17.2307

Mathematical Reviews number (MathSciNet)
MR3686399

Zentralblatt MATH identifier
06762692

Citation

Malkiewich, Cary. Cyclotomic structure in the topological Hochschild homology of $DX$. Algebr. Geom. Topol. 17 (2017), no. 4, 2307--2356. doi:10.2140/agt.2017.17.2307. https://projecteuclid.org/euclid.agt/1510841444

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