Principal Symbol Calculus on Contact Manifolds - Couverture souple

Kordyukov, Yuri; Sukochev, Fedor; Zanin, Dmitriy

Couverture souple

ISBN 10 : 3031699254 ISBN 13 : 9783031699252

Editeur : Springer, 2024

Synopsis

This book develops a C*-algebraic approach to the notion of principal symbol on Heisenberg groups and, using the fact that contact manifolds are locally modeled by Heisenberg groups, on compact contact manifolds. Applying abstract theorems due to Lord, Sukochev, Zanin and McDonald, a principal symbol on the Heisenberg group is introduced as a homomorphism of C*-algebras. This leads to a version of Connes’ trace theorem for Heisenberg groups, followed by a proof of the equivariant behavior of the principal symbol under Heisenberg diffeomorphisms. Using this equivariance and the authors’ globalization theorem, techniques are developed which enable further extensions to arbitrary stratified Lie groups and, as a consequence, the notion of a principal symbol on compact contact manifolds is described via a patching process. Finally, the Connes trace formula on compact contact sub-Riemannian manifolds is established and a spectrally correct version of the sub-Riemannian volume is defined (different from Popp's measure).

The book is aimed at graduate students and researchers working in spectral theory, Heisenberg analysis, operator algebras and noncommutative geometry.

A propos du livre

À propos de l'auteur

Dmitriy Zanin is an author of 100+ papers in non-commutative analysis. This includes the monograph "Singular traces" (written in collaboration with Steven Lord, Edward McDonald and Fedor Sukochev). The key discovery of Dr Zanin is the C*-algebraic nature of the principal symbol.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2024
• Langue: anglais
• ISBN 10: 3031699254
• ISBN 13: 9783031699252
• Reliure: Broché
• Nombre de pages: 172
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne