Higher Structures in Geometry and Physics

In Honor of Murray Gerstenhaber and Jim Stasheff

By: Alberto S. Cattaneo (Editor), Anthony Giaquinto (Editor), Ping Xu (Editor)

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Hardcover | 3 December 2010

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380 Pages

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23.5 x 15.88 x 2.54

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This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics- such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics- and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformation quantization, theory of algebroids and groupoids, symplectic field theory, and much more. The ideas of higher homotopies and algebraic deformation have a growing number of theoretical applications and have played a prominent role in recent mathematical advances. For example, algebraic versions of higher homotopies have led eventually to the proof of the formality conjecture and the deformation quantization of Poisson manifolds. As observed in deformations and deformation philosophy, a basic observation is that higher homotopy structures behave much better than strict structures.

Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. Higher Structures in Geometry and Physics is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures.

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Foreword	p. VII
Preface	p. IX
List of Contributors	p. XIII
Topics in Algebraic Deformation Theory	p. 1
Origins and Breadth of the Theory of Higher Homotopies	p. 25
The Deformation Philosophy, Quantization and Noncommutative Space-Time Structures	p. 39
Differential Geometry of Gerbes and Differential Forms	p. 57
Symplectic Connections of Ricci Type and Star Products	p. 93
Effective Batalin-Vilkovisky Theories, Equivariant Configuration Spaces and Cyclic Chains	p. 111
Noncommutative Calculus and the Gauss-Manin Connection	p. 139
The Lie Algebra Perturbation Lemma	p. 159
Twisting Elements in Homotopy G-Algebras	p. 181
Homological Perturbation Theory and Homological Mirror Symmetry	p. 201
Categorification of Acyclic Cluster Algebras: An Introduction	p. 227
Poisson and Symplectic Functions in Lie Algebroid Theory	p. 243
The Diagonal of the Stasheff Polytope	p. 269
Permutahedra, HKR Isomorphism and Polydifferential Gerstenhaber-Schack Complex	p. 293
Applications de la bi-quantification à la théorie de Lie	p. 315
Higher Homotopy Hopf Algebras Found: A Ten-Year Retrospective	p. 343
Table of Contents provided by Ingram. All Rights Reserved.

Higher Structures in Geometry and Physics

In Honor of Murray Gerstenhaber and Jim Stasheff

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Topology

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Para-HyperKahler Geometry of the Deformation Space of Maximal Globally Hyperbolic Anti-de Sitter Three-Manifolds

The Global Solutions to a Cartan's Realization Problem

Weinstein Handlebodies for Complements of Smoothed Toric Divisors

Mapping Analytic Surgery to Homology, Higher Rho Numbers and Metrics ofPositive Scalar Curvature

The Practice of Algebraic Curves

A Second Course in Algebraic Geometry

Measure Theory and Integration

ADVANCED CALCULUS (REV ED)

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Morse Index of Minimal Submanifolds

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An Introduction to Module Theory

Oxford Graduate Texts in Mathematics

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