Cyclotomic structure in the topological Hochschild homology of DX

Malkiewich, Cary¹

¹Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, United States

Algebraic and Geometric Topology, Tome 17 (2017) no. 4, pp. 2307-2356

Résumé

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.

Détail

DOI : 10.2140/agt.2017.17.2307

Classification : 19D55, 55P43, 55P25, 55P91
Keywords: topological Hochschild homology, cyclotomic spectra, multiplicative norm, geometric fixed points of orthogonal spectra

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