Higher structures in geometry and physics: in honor of Murray Gerstenhaber and Jim Stasheff

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. Theideas of higher homotopies and algebraic deformation have a growing number oftheoretical 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 betterthan strict structures. Each contribution in this volume expands on the ideasof 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. Expository articles on seminal concepts from a rich and variety of research fields Written by distinguished researchers and exeptional speakers Discusses fundamental research and new directions for growth INDICE: Topics in Algebraic deformation theory.- Origins and breadth of the theory of higher homotopies.- The deformation philosophy, quantization and noncommutative space-time structures.- Differential geometry of Gerbes and differential forms.- Symplectic connections of Ricci type and star products.- Effective Batalin–Vilkovisky theories, equivariant configuration spaces and cyclicchains.- Noncommutative calculus and the Gauss-Manin connection.- The Lie algebra perturbation lemma.- Twisting Elements in Homotopy G-algebras.- Homological perturbation theory and homological mirror symmetry.- Categorification of acyclic cluster algebras: an introduction.- Poisson and symplectic functions inLie algebroid theory.- The diagonal of the Stasheff polytope.- Permutahedra, HKR isomorphism and polydifferential Gerstenhaber-Schack complex.- Applications de la bi-quantification a la théorie de Lie.- Higher homotopy Hopf algebras found: A ten year retrospective

• ISBN: 978-0-8176-4734-6
• Editorial: Birkhaüser
• Encuadernacion: Cartoné
• Páginas: 330
• Fecha Publicación: 29/12/2010
• Nº Volúmenes: 1
• Idioma: Inglés