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

作者：Goffeng Magnus^*

来源：Advances in Mathematics, 2012, 231(1): 357-377.

DOI：10.1016/j.aim.2012.05.009

• Regularized index formulas
• Toeplitz operators
• Integral representations of holomorphic functions
• Index theory
• Cyclic cohomology

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 Holder continuous symbol. The index formula gives an analytic formula for the degree of a Holder continuous mapping from the boundary of a strictly pseudo-convex domain.

• 出版日期2012-9-10