Families of Legendrian submanifolds via generating families

Abstract

We investigate families of Legendrian submanifolds in 1-jet spaces by developing and applying a theory of families of generating family homologies. This theory allows us to detect an infinite family of loops of Legendrian $n$-spheres embedded in the standard contact ${\mathbb{R}}^{2n+1}$ (for $n>1$) that are contractible in the smooth, but not Legendrian, category.