Operads in algebra, topology and physics

Description

This exposition of the theory of finite Hopf spaces details the development of the subject over the last thirty years, with the homology of such spaces as its main theme. The three chief areas of study in the volume are: - The study of finite H-spaces with torsion free integral homology. - The study of finite H-spaces with homology torsion. - The construction of finite H-spaces Introduction and History -- A prehistory -- Lazard's formal group laws -- PROPs and PACTs -- Non-[Sigma] operads and operads -- Theories -- Tree operads -- A[subscript [infinity]-spaces and loop spaces -- E[subscript [infinity]-spaces and iterated loop spaces -- A[subscript [infinity]-algebras -- Partiality and A[subscript [infinity]-categories -- L[subscript [infinity]-algebras -- C[subscript [infinity]-algebras -- n-ary algebras -- Operadic bar construction and Koszul duality -- Cyclic operads -- Moduli spaces and modular operads -- Operadic interpretation of closed string field theory -- From topological operads to dg operads -- Homotopy invariance in algebra and topology -- Formality, quantization and Deligne's conjecture -- Insertion operads -- Operads in a Symmetric Monoidal Category -- Symmetric monoidal categories -- Operads -- Pseudo-operads -- Operad algebras -- The pseudo-operad of labeled rooted trees -- The Stasheff associahedra -- Operads defined in terms of arbitrary finite sets -- Operads as monoids -- Free operads and free pseudo-operads -- Collections, K-collections and K-operads -- The GK-construction -- Triples -- Topology--Review of Classical Results -- Iterated loop spaces -- Recognition -- The bar construction: theme and variations -- Approximation -- [Gamma]-spaces -- Homology operations -- The linear isometries operad and infinite loop spaces -- W-construction -- Algebraic structures up to strong homotopy -- Algebra -- The cobar complex of an operad -- Quadratic operads -- Koszul operads