Cyclotomic structure in the topological Hochschild homology of $DX$

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 ${\Sigma }_{+}^{\infty }LX$ 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.

arXiv commentAccepted version, 46 pages. Replaces the first half of the earlier preprint "On the topological Hochschild homology of $DX$." Part of the author's thesis

References in corpus (3)

• On an extension of the notion of Reedy category
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Cited by in corpus (2)

• Comparing cyclotomic structures on different models for topological Hochschild homology
• Periodic points and topological restriction homology