Analysis on singular spaces: Lie manifolds and operator algebras

Victor Nistor

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

We discuss and develop some connections between analysis on singular spaces and operator algebras, as presented in my sequence of four lectures at the conference Noncommutative geometry and applications, Frascati, Italy, June 16–21, 2014. Therefore this paper is mostly a survey paper, but the presentation is new, and there are included some new results as well. In particular, Sections 3 and 4 provide a complete short introduction to analysis on noncompact manifolds that is geared towards a class of manifolds–called “Lie manifolds” –that often appears in practice. Our interest in Lie manifolds is due to the fact that they provide the link between analysis on singular spaces and operator algebras. The groupoids integrating Lie manifolds play an important background role in establishing this link because they provide operator algebras whose structure is often well understood. The initial motivation for the work surveyed here–work that spans over close to two decades–was to develop the index theory of stratified singular spaces. Meanwhile, several other applications have emerged as well, including applications to Partial Differential Equations and Numerical Methods. These will be mentioned only briefly, however, due to the lack of space. Instead, we shall concentrate on the applications to Index theory.

Original languageEnglish (US)
Pages (from-to)75-101
Number of pages27
JournalJournal of Geometry and Physics
Volume105
DOIs
StatePublished - Jul 2016

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

Fingerprint Dive into the research topics of 'Analysis on singular spaces: Lie manifolds and operator algebras'. Together they form a unique fingerprint.

  • Cite this