Analysis, geometry and topology of elliptic operators / editors, Bernhelm Booss-Bavnbek ... [et al.].

Format:

Book

Contributor:

Booss, Bernhelm, 1941-

Wojciechowski, Krzysztof P., 1953-

Language:

English

Subjects (All):

Elliptic operators.

Differential equations, Elliptic.

Topology.

Boundary value problems.

Physical Description:

1 online resource (553 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; Hackensack, NJ : World Scientific, c2006.

Language Note:

English

Summary:

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 achievem

Contents:

Contents ; Preface ; Part I. On the Mathematical Work of Krzysztof P. ; Selected Aspects of the Mathematical Work of Krzysztof P.Wojciechowski ; Gluing Formulae of Spectral Invariants and Cauchy Data Spaces ; Part II. Topological Theories

The Behavior of the Analytic Index under Nontrivial Embedding Critical Points of Polynomials in Three Complex Variables ; Chern-Weil Forms Associated with Superconnections ; Part III. Heat Kernel Calculations and Surgery ; Non-Laplace Type Operators on Manifolds with Boundary

Eta Invariants for Manifold with Boundary Heat Kernels of the Sub-Laplacian and the Laplacian on Nilpotent Lie Groups ; Remarks on Nonlocal Trace Expansion Coefficients ; An Anomaly Formula for L2-Analytic Torsions on Manifolds with Boundary ; Conformal Anomalies via Canonical Traces

Part IV. Noncommutative Geometry An Analytic Approach to Spectral Flow in von Neumann Algebras ; Elliptic Operators on Infinite Graphs ; A New Kind of Index Theorem ; A Note on Noncommutative Holomorphic and Harmonic Functions on the Unit Disk ; Star Products and Central Extensions

An Elementary Proof of the Homotopy Equivalence between the Restricted General Linear Group and the Space of Fredholm Operators Part V. Theoretical Particle String and Membrane Physics and Hamiltonian Dynamics ; T-DUALITY FOR NON-FREE CIRCLE ACTIONS

A New Spectral Cancellation in Quantum Gravity

Notes:

"On May 20-22, 2005, a workshop was held at Roskilde University in Denmark to honour Krzysztof P. Wojciechowski on his 50th birthday. This volume collects the papers of that workshop"--P. ix.

Includes bibliographical references.

ISBN:

9786611379001

9781281379009

128137900X

9789812773609

9812773606

OCLC:

748527948