Homotopy Frobenius structures on the cohomology of a manifold

Florian Naef; Thomas Willwacher

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arXiv · 2606.28466

Homotopy Frobenius structures on the cohomology of a manifold

Florian Naef·Thomas Willwacher

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Abstract

We show that the category of lax involutive $n$-Frobenius algebras is Quillen equivalent to the category of right comodules of the $n$-Poisson cooperad. It follows in particular, that the cohomology of a parallelized $n$-manifold is naturally endowed with a homotopy involutive $n$-Frobenius structure extending the rational homotopy type of $M$, solving a long-standing question.

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Florian Naef, Thomas Willwacher. 2026-06-26. Homotopy Frobenius structures on the cohomology of a manifold. https://arxiv.org/abs/2606.28466

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