A Smale Type Result and Applications to Contact Homology

Abstract

In this note we will show that the injection of a suitable subspace of the space of Legendrian loops into the full loop space is an S 1 -equivariant homotopy equivalence. Moreover, since the smaller space is the space of variations of a given action functional, we will compute the relative Contact Homology of a family of tight contact forms on the three-dimensional torus.