Boundary framings for locally conformally symplectic four-manifolds

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 ($\S 2$, generalizing contact structures). Powerful $s{l}_2$ - 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.

Extensively revised, but the introduction is at the end