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arXiv · 2502.05983

Boundary framings for locally conformally symplectic four-manifolds

J Morava
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Abstract

We construct a rational homotopy-theoretic model for a classifying space of locally conformally symplectic structures on four-manifolds, and use it to definition a cobordism category of three-manifolds `anchored' by principal $\Omega^2 S^2$ - bundles ($\S2$, generalizing contact structures). Powerful $sl_2$ - representation-valued Hodge-Lefschetz cohomology (going back to Chern and Weil), taking values in the $\mathbb{Z}$-graded category of bidifferential modules of Angella, Otiman, and Tardini is available for its study. This is an extended revision with a detailed introduction replacing the final section. The original concern of the paper was a characteristic two issue which remains unchanged.

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J Morava. 2025-02-09. Boundary framings for locally conformally symplectic four-manifolds. https://arxiv.org/abs/2502.05983

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