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arXiv · 2608.20289

Spectral Viterbo isomorphism: complex-oriented versus framed

Kenneth Blakey
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Abstract

The Viterbo isomorphism relates the symplectic cohomology of a cotangent bundle to the homology of the free loop space of its base. We lift this to a relation of modules over (1) the complex bordism spectrum MU and (2) the sphere spectrum $\mathbb{S}$. In particular, by a result of Porcelli and the present author [BP26], it is not the case that, in general, the $\mathbb{S}$-level statement recovers the MU-level statement after base-change -- even in the case the base is spin.

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Kenneth Blakey. 2026-08-20. Spectral Viterbo isomorphism: complex-oriented versus framed. https://arxiv.org/abs/2608.20289

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