Geometry and topology of group actions on symplectic and contact manifolds

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

DMS-0204448 Eugene Lerman and Susan Tolman The main subject of our proposal in the geometry and topology of group actions on symplectic and contact manifolds. The underlying theme is that these symmetries offer a very powerful tool for classifying or computing invariants of such manifolds. More specifically, ideas that we will investigate include: the cohomology of symplectic quotients by loop groups, the cohomology of contact quotients, highly symmetric manifolds, the Gromov width of coadjoint orbits, the topology of the group of symplectomorphisms, uniruled symplectic manifolds, foundational work on group actions on contact manifolds, the relationship between completely integrable systems and toric contact manifolds, and explicit constructions of special metrics on contact manifolds. The goal of the project is to further our understanding of two important types of geometry --- symplectic and contact. Both geometries have their origins in mechanics and optics and are currently of interest to physicists investigating string theories.