Analysis, Geometry And Topology Of Elliptic Operators: Papers In Honor Of Krzysztof P Wojciechowski

by Matthias Lesch, Weiping Zhang, Slawomir Klimek, Bernhelm Booss-bavnbek

Overview

Modern theory of elliptic operators, or simply elliptic theory, has been shaped by the Atiyah-Singer Index Theorem created 40 years ago. Reviewing elliptic theory over a broad range, 32 leading scientists from 14 different countries present recent developments in topology; heat kernel techniques; spectral invariants and cutting and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics.The first of its kind, this volume is ideally suited to graduate students and researchers interested in careful expositions of newly-evolved achievements and perspectives in elliptic theory. The contributions are based on lectures presented at a workshop acknowledging Krzysztof P Wojciechowski's work in the theory of elliptic operators.

Product Details

ISBN-13:	9789812568052
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	04/26/2006
Pages:	552
Product dimensions:	6.20(w) x 9.00(h) x 1.30(d)

Table of Contents

Preface ix

Part I On the Mathematical Work of Krzysztof P. Wojciechowski

Selected Aspects of the Mathematical Work of Krzysztof P. Wojciechowski Matthias Lesch 3

Gluing Formulae of Spectral Invariants and Cauchy Data Spaces Jinsung Park 23

Part II Topological Theories

The Behavior of the Analytic Index under Nontrivial Embedding David Bleecker 41

Critical Points of Polynomials in Three Complex Variables Liviu I. Nicolaescu 63

Chern-Weil Forms Associated with Superconnections Sylvie Paycha Simon Scott 79

Part III Heat Kernel Calculations and Surgery

Non-Laplace Type Operators on Manifolds with Boundary Ivan G. Avramidi 107

Eta Invariants for Manifold with Boundary Xianzhe Dai 141

Heat Kernels of the Sub-Laplacian and the Laplacian on Nilpotent Lie Groups Kenro Furutani 173

Remarks on Nonlocal Trace Expansion Coefficients Gerd Grubb 215

An Anomaly Formula for L[superscript 2]-Analytic Torsions on Manifolds with Boundary Xiaonan Ma Weiping Zhang 235

Conformal Anomalies via Canonical Traces Sylvie Paycha Steven Rosenberg 263

Part IV Noncommutative Geometry

An Analytic Approach to Spectral Flow in von Neumann Algebras Moulay-Tahar Benameur Alan L. Carey John Phillips Adam Rennie Fyodor A. Sukochev Krzysztof P. Wojciechowski 297

Elliptic Operators on Infinite Graphs Jozef Dodziuk 353

A New Kind of Index Theorem Ronald G. Douglas 369

A Note on Noncommutative Holomorphic and Harmonic Functions on the Unit Disk Slawomir Klimek 383

Star Products and Central Extensions Jouko Mickelsson 401

An Elementary Proof of the Homotopy Equivalence between the Restricted General Linear Group and the Space of Fredholm Operators Tilmann Wurzbacher 411

Part V TheoreticalParticle, String and Membrane Physics, and Hamiltonian Dynamics

T-Duality for Non-Free Circle Actions Ulrich Bunke Thomas Schick 429

A New Spectral Cancellation in Quantum Gravity Giampiero Esposito Guglielmo Fucci Alexander Kamenshchik Klaus Kirsten 467

A Generalized Morse Index Theorem Chaofeng Zhu 493