M/υ

Given a three dimensional closed contact manifold (M³, α) and a nowhere singular Morse vector-field υ in its kernel, we sketch the construction of the space M/υ discussed in [4]. We also introduce spaces of immersed curves in M/υ and an action functional on these spaces. This is the first step in the completion of a program aimed at computing the homology for contact forms defined in [2] and [7].