Operads In Algebra Topology And Physics

Author : Martin Markl
Publisher : American Mathematical Soc.
ISBN 13 : 0821843621
Total Pages : 362 pages
Book Rating : 4.28/5 ( download)

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Download or read book Operads in Algebra, Topology and Physics written by Martin Markl and published by American Mathematical Soc.. This book was released on 2002 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Operads are mathematical devices which describe algebraic structures of many varieties and in various categories. From their beginnings in the 1960s, they have developed to encompass such areas as combinatorics, knot theory, moduli spaces, string field theory and deformation quantization.

Author : Martin Markl
Publisher : American Mathematical Society(RI)
ISBN 13 : 9781470413231
Total Pages : 362 pages
Book Rating : 4.3X/5 ( download)

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Download or read book Operads in Algebra, Topology, and Physics written by Martin Markl and published by American Mathematical Society(RI). This book was released on 2014-05-21 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Operads are mathematical devices which describe algebraic structures of many varieties and in various categories. Operads are particularly important in categories with a good notion of homotopy where they play a key role in organizing hierarchies of higher homotopies. Significant examples first appeared in the 1960s, though the formal definition and appropriate generality waited until a decade later. These early occurrences were in algebraic topology in the study of (iterated) loop spaces and their chain algebras.

Author : Jean-Louis Loday
Publisher : Springer Science & Business Media
ISBN 13 : 3642303625
Total Pages : 649 pages
Book Rating : 4.23/5 ( download)

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Download or read book Algebraic Operads written by Jean-Louis Loday and published by Springer Science & Business Media. This book was released on 2012-08-08 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many areas of mathematics some “higher operations” are arising. These havebecome so important that several research projects refer to such expressions. Higher operationsform new types of algebras. The key to understanding and comparing them, to creating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such as algebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study all kinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a conceptual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality for associative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the Homotopy Transfer Theorem. Although the necessary notions of algebra are recalled, readers are expected to be familiar with elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and numerous figures are included. After a low-level chapter on Algebra, accessible to (advanced) undergraduate students, the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three appendices review the basic results needed in order to understand the various chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, the book can also be used as a reference work by researchers.

Author : Bai Chengming
Publisher : World Scientific
ISBN 13 : 9814458333
Total Pages : 320 pages
Book Rating : 4.37/5 ( download)

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Download or read book Operads And Universal Algebra - Proceedings Of The International Conference written by Bai Chengming and published by World Scientific. This book was released on 2012-02-23 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims to exemplify the recent developments in operad theory, in universal algebra and related topics in algebraic topology and theoretical physics. The conference has established a better connection between mathematicians working on operads (mainly the French team) and mathematicians working in universal algebra (primarily the Chinese team), and to exchange problems, methods and techniques from these two subject areas.

Author : Benoit Fresse
Publisher : American Mathematical Soc.
ISBN 13 : 1470434822
Total Pages : 704 pages
Book Rating : 4.23/5 ( download)

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Download or read book Homotopy of Operads and Grothendieck-Teichmuller Groups written by Benoit Fresse and published by American Mathematical Soc.. This book was released on 2017-05-22 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ultimate goal of this book is to explain that the Grothendieck–Teichmüller group, as defined by Drinfeld in quantum group theory, has a topological interpretation as a group of homotopy automorphisms associated to the little 2-disc operad. To establish this result, the applications of methods of algebraic topology to operads must be developed. This volume is devoted primarily to this subject, with the main objective of developing a rational homotopy theory for operads. The book starts with a comprehensive review of the general theory of model categories and of general methods of homotopy theory. The definition of the Sullivan model for the rational homotopy of spaces is revisited, and the definition of models for the rational homotopy of operads is then explained. The applications of spectral sequence methods to compute homotopy automorphism spaces associated to operads are also explained. This approach is used to get a topological interpretation of the Grothendieck–Teichmüller group in the case of the little 2-disc operad. This volume is intended for graduate students and researchers interested in the applications of homotopy theory methods in operad theory. It is accessible to readers with a minimal background in classical algebraic topology and operad theory.

Author : Tom Leinster
Publisher : Cambridge University Press
ISBN 13 : 0521532159
Total Pages : 451 pages
Book Rating : 4.50/5 ( download)

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Download or read book Higher Operads, Higher Categories written by Tom Leinster and published by Cambridge University Press. This book was released on 2004-07-22 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of higher dimensional category theory for graduate students and researchers in mathematics and mathematical physics.

Author : James D. Stasheff
Publisher : American Mathematical Soc.
ISBN 13 : 082180913X
Total Pages : 338 pages
Book Rating : 4.36/5 ( download)

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Download or read book Higher Homotopy Structures in Topology and Mathematical Physics written by James D. Stasheff and published by American Mathematical Soc.. This book was released on 1999 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the work of Stasheff and Sugawara in the 1960s on recognition of loop space structures on $H$-spaces, the notion of higher homotopies has grown to be a fundamental organizing principle in homotopy theory, differential graded homological algebra and even mathematical physics. This book presents the proceedings from a conference held on the occasion of Stasheff's 60th birthday at Vassar in June 1996. It offers a collection of very high quality papers and includes some fundamental essays on topics that open new areas.

Author : Jean-Louis Loday
Publisher : American Mathematical Soc.
ISBN 13 : 9780821855386
Total Pages : 460 pages
Book Rating : 4.87/5 ( download)

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Download or read book Operads written by Jean-Louis Loday and published by American Mathematical Soc.. This book was released on 1996-12-13 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: ``Operads'' are mathematical devices which model many sorts of algebras (such as associative, commutative, Lie, Poisson, alternative, Leibniz, etc., including those defined up to homotopy, such as $A_{\infty}$-algebras). Since the notion of an operad appeared in the seventies in algebraic topology, there has been a renaissance of this theory due to the discovery of relationships with graph cohomology, Koszul duality, representation theory, combinatorics, cyclic cohomology, moduli spaces, knot theory, and quantum field theory. This renaissance was recognized at a special session ``Moduli Spaces, Operads, and Representation Theory'' of the AMS meeting in Hartford, CT (March 1995), and at a conference ``Operades et Algebre Homotopique'' held at the Centre International de Rencontres Mathematiques at Luminy, France (May-June 1995). Both meetings drew a diverse group of researchers. The authors have arranged the contributions so as to emphasize certain themes around which the renaissance of operads took place: homotopy algebra, algebraic topology, polyhedra and combinatorics, and applications to physics.

Author : Benoit Fresse
Publisher : Springer Science & Business Media
ISBN 13 : 3540890556
Total Pages : 304 pages
Book Rating : 4.53/5 ( download)

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Download or read book Modules Over Operads and Functors written by Benoit Fresse and published by Springer Science & Business Media. This book was released on 2009-03-26 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of an operad supplies both a conceptual and effective device to handle a variety of algebraic structures in various situations. Operads were introduced 40 years ago in algebraic topology in order to model the structure of iterated loop spaces. Since then, operads have been used fruitfully in many fields of mathematics and physics. This monograph begins with a review of the basis of operad theory. The main purpose is to study structures of modules over operads as a new device to model functors between categories of algebras as effectively as operads model categories of algebras.

Author : Daniel S. Freed
Publisher : American Mathematical Soc.
ISBN 13 : 1470452065
Total Pages : 186 pages
Book Rating : 4.63/5 ( download)

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Download or read book Lectures on Field Theory and Topology written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2019-08-23 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.