Laurence Mayther (Cambridge) will talk in the geometry seminar on 27th November, at 2pm in the Salle des Profs. Laurence’s title is “New h-Principles in [split]G2, Symplectic and Contact Geometry” and his abstract is below.
An exterior form is termed stable if its algebraic properties are preserved by all sufficiently small perturbations. Stable forms are fundamental to the study of G2/[split]G2 geometry and symplectic geometry, and also play a key role in the study of contact geometry.
In this talk, I shall introduce a new, general method for proving h-principles for stable forms, building on Gromov’s technique of convex integration, and use this to prove 4 new h-principles related to these geometries. Applications to the non-constructability of compact [split]G2 and symplectic manifolds via geometric flows will then be discussed. Time permitting, I shall also explain how this new method for proving h-principles subsumes all similar, previously established h-principles, and explain how it may be extended to prove a fifth new h-principle in 6-dimensions related to para-complex structures.