Description
BIRKHAUSER Higher Structures In Geometry And Physics In Honor Of Murray Gerstenhaber And Jim Stasheff 2010 Edition by Alberto S. Cattaneo Anthony Giaquinto Ping Xu
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. Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. The volume is intended for post-graduate students mathematical and theoretical physicists and mathematicians interested in higher structures. Table of contents : 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 cyclic chains.- 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 in Lie algebroid theory.- The diagonal of the Stasheff polytope.- Permutahedra HKR isomorphism and polydifferential Gerstenhaber-Schack complex.- Applications de la bi-quantification a la theorie de Lie.- Higher homotopy Hopf algebras found: A ten year retrospective