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 sl_2 - representation-valued Hodge-Lefschetz cohomology (going back to Chern and Weil), taking values in the \Z-graded category of bidifferential modules of Angella, Otiman, and Tardini is available for its study. \S3 observes that Ebin's configuration groupoid [Metrics/Dif] for Euclidean general relativity can be represented (cohomologically over $\Q$) in terms of a category of objects (or `aspects') of $X$ (as a space, under the action of its group of (pointed, etc) diffeomorphisms). This provides a notational system for the higher category of actions of compact connected groups $K$ on $X$, which is classically accessible by Atiyah-Bott/Duistermaat-Heckmann localisation.

Locations

• arXiv (Cornell University) - View - PDF