Analytic formulas for topological degree of non-smooth mappings: the odd-dimensional case

The notion of topological degree is studied for mappings from the boundary of a relatively compact strictly pseudo-convex domain in a Stein manifold into a manifold in terms of index theory of Toeplitz operators on the Hardy space. The index formalism of non-commutative geometry is used to derive analytic integral formulas for the index of a Toeplitz operator with H\"older continuous symbol. The index formula gives an analytic formula for the degree of a H\"older continuous mapping from the boundary of a strictly pseudo-convex domain.