Spectral Triples and manifolds with boundaries

Abstract:

The purpose is to present a survey (no details) within the noncommutative geometry framework of Connes on two different approaches for manifolds with boundaries. The objective is to construct spectral triples in two cases:  the first one concerns the Boutet de Monvel boundary pseudodifferential calculus for real manifolds while the second pays attention the Cauchy-Riemann structures on pseudoconvex bounded domains with an application to the Berezin-Toeplitz quantization.