Mathematical Sciences: Studies in Non-Commutative Geometry

点击翻译按钮获取中文摘要

9401192 Moscovici The proposed research aims to: (1) develop an Alexander-Spanier version of the Chern character; (2) obtain explicit local formulae for the Pontryagin classes of topological manifolds; (3) develop a theory of straight characteristic classes for foliations of Lipschitz manifolds; (4) obtain residual index formulae for abstract elliptic operators in terms of the Dixmier trace; (5) recover the holomorphic torsion of a Hermitian locally symmetric manifold by means of a geometric zeta function. The "quantized" differential and integral calculus, recently invented by Alain Connes, will be applied to the treatment of certain open problems in several areas of mathematics -topology, geometry and operator algebras. ***