For every variety X with a C* action there exists a moduli space parameterizing the broken flow lines of the C* action. Part of the homology of this space forms a ring which can be computed in terms of the data of the C* action. Moreover this ring can be used to describe the intersection ring of X, the equivarint cohomology of X and the Gromov-Witten invariants of X. This is joint work with Anca Mustata.