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.
Author(s): Matthias Lesch, Bernhelm Boo-Bavnbek, Slawomir Klimek, Weiping Zhang
Publisher: World Scientific Publishing Company
Year: 2006
Language: English
Pages: 553
Tags: Математика;Функциональный анализ;
Contents......Page 6
Preface......Page 10
Part I. On the Mathematical Work of Krzysztof P.......Page 13
Selected Aspects of the Mathematical Work of Krzysztof P.Wojciechowski......Page 15
Gluing Formulae of Spectral Invariants and Cauchy Data Spaces......Page 35
Part II. Topological Theories......Page 51
The Behavior of the Analytic Index under Nontrivial Embedding......Page 53
Critical Points of Polynomials in Three Complex Variables......Page 75
Chern-Weil Forms Associated with Superconnections......Page 91
Part III. Heat Kernel Calculations and Surgery......Page 117
Non-Laplace Type Operators on Manifolds with Boundary......Page 119
Eta Invariants for Manifold with Boundary......Page 153
Heat Kernels of the Sub-Laplacian and the Laplacian on Nilpotent Lie Groups......Page 185
Remarks on Nonlocal Trace Expansion Coefficients......Page 227
An Anomaly Formula for L2-Analytic Torsions on Manifolds with Boundary......Page 247
Conformal Anomalies via Canonical Traces......Page 275
Part IV. Noncommutative Geometry......Page 307
An Analytic Approach to Spectral Flow in von Neumann Algebras......Page 309
Elliptic Operators on Infinite Graphs......Page 365
A New Kind of Index Theorem......Page 381
A Note on Noncommutative Holomorphic and Harmonic Functions on the Unit Disk......Page 395
Star Products and Central Extensions......Page 413
An Elementary Proof of the Homotopy Equivalence between the Restricted General Linear Group and the Space of Fredholm Operators......Page 423
Part V. Theoretical Particle String and Membrane Physics and Hamiltonian Dynamics......Page 439
T-DUALITY FOR NON-FREE CIRCLE ACTIONS......Page 441
A New Spectral Cancellation in Quantum Gravity......Page 479
A Generalized Morse Index Theorem......Page 505
