NONCOMMUTATIVE GEOMETRY ON TREES AND BUILDINGS

Abstract

The notion of a spectral triple, introduced by Connes (cf. [9], [7], [10]), provides a powerful generalization of Riemannian geometry to noncommutative spaces. It originates from the observation that, on a smooth compact spin manifold, the infinitesimal line element ds can be expressed in terms of the inverse of the classical Dirac operator D, so that the Riemannia