The Liouville phenomenon in the deformation of coisotropic submanifolds

Abstract

Deformation of coisotropic submanifolds involves significant subtleties not present in the deformation of Lagrangian submanifolds. Oh and Park's L ∞ -algebra provides an explicit computational tool for teasing out these subtleties, and here we revisit and complete their main example. We find that the obstruction theory of this L ∞ -algebra succeeds in making a fine distinction among foliations with infinite holonomy involving the Liouville phenomenon. We also find a suggestive connection with the geometry of Haefliger's model Ω c ∗ ( T / H ) for the reduced space.