Topological quantum mechanical symmetries

The notion of a topological quantum mechanical symmetry (topological symmetry, in brief) is introduced. A topological symmetry is a generalization of supersymmetry and involves some topological invariants like Witten index. The algebraic structure of Z2 graded topological symmetry's of type (m+ , m-) is obtained and it is shown that for topological symmetry's of type (1,1) and (2,1) they are identical to algebraic structure of supersymmetry and p=2 para supersymmetry respectively