Principal symbol calculus on contact manifolds / Yuri Kordyukov, Fedor Sukochev, Dmitriy Zanin.

Format:

Book

Author/Creator:

Kordyukov, Yuri, author.

Sukochev, F. A., author.

Zanin, Dmitriy, author.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2359.

Lecture notes in mathematics, 0075-8434 ; volume 2359

Language:

English

Subjects (All):

C*-algebras.

Physical Description:

xiv, 154 pages ; 24 cm.

Place of Publication:

Cham, Switzerland : Springer, [2024]

Summary:

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.

Contents:

Preface

Foreword by Nigel Higson

Introduction

Principal Symbol on the Heisenberg Group

Equivariance of the Principal Symbol Under Heisenberg Diffeomorphisms

Principal Symbol on Contact Manifolds

Bibliography.

Notes:

Includes bibliographical references.

ISBN:

9783031699252

3031699254

OCLC:

1463608703