The Library of Congress > Linked Data Service > BIBFRAME Works

Bibframe Work

Title
The Connes character formula for locally compact spectral triples
Type
Text
Monograph
Contribution
Sukochev, F. A. (Author)
Zanin, Dmitriy (Author)
Subject
Noncommutative differential geometry (LCSH)
Functional analysis (LCSH)
Spectral sequences (Mathematics) (LCSH)
Chern classes (LCSH)
Géométrie différentielle non commutative (RVM)
Analyse fonctionnelle (RVM)
Suites spectrales (Mathématiques) (RVM)
Classes de Chern (RVM)
Hochschild character theorem
Hochschild cohomology
Spectral triples
Singular traces
Heat semigroup
Chern character
Language
English
Could not render: rdf:value
Could not render: bf:part
Could not render: rdf:value
Classification
LCC: QC20.7.D52 S85 2023 (Assigner: dlc) (Status: used by assigner)
Supplementary Content
bibliography
Content
text
Note
Includes translation
Language: In English; abstract also in French.
Summary
"A fundamental tool in noncommutative geometry is Connes's character formula. This formula is used in an essential way in the applications of noncommutative geometry to index theory and to the spectral characterization of manifolds. A non-compact space is modeled in noncommutative geometry by a non-unital spectral triple. The authors' aim is to establish Connes's character formula for non-unital spectral triples. This is significantly more difficult than in the unital case, and they achieve it with the use of recently developed double operator integration techniques. Previously, only partial extensions of Connes's character formula to the non-unital case were known. In the course of the proof, the authors establish two more results of importance in noncommutative geometry: an asymptotic for the heat semigroup of a non-unital spectral triple and the analyticity of the associated [Riemann zeta] function. The authors require certain assumptions on the underlying spectral triple and verify these assumptions in the case of spectral triples associated to arbitrary complete Riemannian manifolds and also in the case of Moyal planes"--American Mathematical Society bookstore website.
Table Of Contents
1. Introduction
2. Preliminaries
3. Spectral triples : basic properties and examples
4. Asymptotic of the heat trace
5. Residue of the [Riemann zeta] function and the Connes character formula
Appendix.
Authorized Access Point
Sukochev, F. A. The Connes character formula for locally compact spectral triples
Admin Metadata
Generation Process: DLC marc2bibframe2 v2.5.0
Status: changed
Encoding Level: minimal
Identified By: bf:Local, 23566513
Change Date: 2024-03-08T12:49:45
Creation Date: 2024-02-20
Description Language: English
Description Modifier: United States, Library of Congress
Description Authentication: LC Copy Cataloging
Assigner: WTU