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

Artikel i vetenskaplig tidskrift, 2013

Topological degrees of continuous mappings between oriented manifolds of even dimension are studied in terms of index theory of pseudo-differential operators. The index formalism of non-commutative geometry is used to derive analytic integral formulas for the index of a 0th order pseudo-differential operator twisted by a Holder continuous complex vector bundle. The index formula gives an analytic formula for the degree of a Holder continuous mapping between even-dimensional oriented manifolds. The paper is an independent continuation of the paper Analytic formulas for topological degree of non-smooth mappings: the odd-dimensional case.