Invariants of topological quantum mechanics

We investigate a new topological invariant of the punctured plane using a Hamiltonian approach. The Hamiltonian is built out of topological invariants available on the punctured plane. On the other hand it is shown that the model is a generalized version, using the appropriate language of homotopy, of the superconformal quantum mechanics (gauge approach) recently proposed by L. Baulieu et al. This relationship allows a better understanding of the structure and results of the gauge approach and makes possible a proper identification of the topological invariants which emerge from it