\(K\)-homology and regular singular Dirac-Schrödinger operators on even-dimensional manifolds
type: Item
instance of: scholarly article
title: \(K\)-homology and regular singular Dirac-Schrödinger operators on even-dimensional manifolds
zbMATH Open document ID: 0909.58047
author: Jeffrey Fox
author: Peter Haskell
published in: Pacific Journal of Mathematics
publication date: 1999-03-21T00:00:00Z
review text: The authors study index problems associated to Dirac type operators on incomplete Riemann manifolds with asymptotically cone-like singularities. The behavior of the Dirac operator near these singularities is restricted by the regular-singular assumption. The authors show that these operators define classes in the \(K\)-homology of the metric completion of such manifolds. These are described as Kasparov products of a \(K\)-homology class on the incomplete manifold and a certain \(K\)-cohomology class determined by the zeroth order part of the operator. Among the tools used in this paper are the analysis of regular-singular operators and techniques for studying analytic \(K\)-homology cycles on singular spaces and their open dense subsets.
Mathematics Subject Classification ID: 58J22
Mathematics Subject Classification ID: 19K35
Mathematics Subject Classification ID: 19K56
zbMATH DE Number: 1136630
zbMATH Keywords: incomplete Riemann manifolds
zbMATH Keywords: conelike singularities
zbMATH Keywords: index theory
zbMATH Keywords: regular-singular operators
zbMATH Keywords: Dirac type operators
zbMATH Keywords: K-homology
zbMATH Keywords: KK-theory
reviewed by: Liviu I. Nicolaescu
MaRDI profile type: Publication
full work available at URL: pjm.1997.180.251
OpenAlex ID: W2100215616
DOI: 10.2140/PJM.1997.180.251
description: scientific article; zbMATH DE number 1136630