This talk was part of the Thematic Programme on "Higher Structures and Field Theory" held at the ESI August 1 to 26, 2022. Deformations of spacelike hypersurfaces in space-time have recently been shown to form an L-infinity algebroid. Space-time models for gravitational field theories, however, are commonly derived and analyzed using a Poisson bracket. The discrepancy may have implications for physics questions such as the nature of black-hole singularities.
Keywords: Hypersurface deformation, Martin Bojowald, Field Theory