Algebraic & Geometric Topology

Cyclotomic structure in the topological Hochschild homology of $DX$

Cary Malkiewich

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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
Received: 17 May 2016
Revised: 21 January 2017
Accepted: 16 February 2017
First available in Project Euclid: 16 November 2017

Permanent link to this document
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

Subjects
Primary: 19D55: $K$-theory and homology; cyclic homology and cohomology [See also 18G60] 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)
Secondary: 55P25: Spanier-Whitehead duality 55P91: Equivariant homotopy theory [See also 19L47]

Keywords
topological Hochschild homology cyclotomic spectra multiplicative norm geometric fixed points of orthogonal spectra

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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