Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 17, Number 4 (2017), 2307-2356.
Cyclotomic structure in the topological Hochschild homology of $DX$
Let be a finite CW complex, and let be its dual in the category of spectra. We demonstrate that the Poincaré/Koszul duality between and the free loop space is in fact a genuinely –equivariant duality that preserves the –fixed points. Our proof uses an elementary but surprisingly useful rigidity theorem for the geometric fixed point functor of orthogonal –spectra.
Algebr. Geom. Topol., Volume 17, Number 4 (2017), 2307-2356.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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