Index Theory For Locally Compact Noncommutative Geometries
Download Index Theory For Locally Compact Noncommutative Geometries PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Index Theory For Locally Compact Noncommutative Geometries book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Index Theory for Locally Compact Noncommutative Geometries
Author: A. L. Carey
language: en
Publisher: American Mathematical Soc.
Release Date: 2014-08-12
Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, the authors prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and the authors illustrate this point with two examples in the text. In order to understand what is new in their approach in the commutative setting the authors prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds their index formula appears to be completely new.
From Differential Geometry to Non-commutative Geometry and Topology
Author: Neculai S. Teleman
language: en
Publisher: Springer Nature
Release Date: 2019-11-10
This book aims to provide a friendly introduction to non-commutative geometry. It studies index theory from a classical differential geometry perspective up to the point where classical differential geometry methods become insufficient. It then presents non-commutative geometry as a natural continuation of classical differential geometry. It thereby aims to provide a natural link between classical differential geometry and non-commutative geometry. The book shows that the index formula is a topological statement, and ends with non-commutative topology.
Geometries in Interaction
In the last decades of the 20th century tremendous progress has been achieved in geometry. The discovery of deep interrelations between geometry and other fields including algebra, analysis and topology has pushed it into the mainstream of modern mathematics. This Special Issue of Geometric And Functional Analysis (GAFA) in honour of Mikhail Gromov contains 14 papers which give a wide panorama of recent fundamental developments in modern geometry and its related subjects. The book is a collection of important results and an enduring source of new ideas for researchers and students in a broad spectrum of directions related to all aspects of geometry and its applications to functional analysis, PDE, analytic number theory and physics. This is a reprint from GAFA, Vol. 5 (1995), No. 2., enlarged by a short biography of Mikhail Gromov and a list of his publications.