Covering an exceptional range of topics, this text provides a unique overview of the Maurer—Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new conceptual treatment of the twisting procedure, guiding the reader through various versions with the help of plentiful motivating examples for graduate students as well as researchers. Topics covered include a novel approach to the twisting procedure for operads leading to Kontsevich graph homology and a description of the twisting procedure for (homotopy) associative algebras or (homotopy) Lie algebras using the biggest deformation gauge group ever considered. The book concludes with concise surveys of recent applications in areas including higher category theory and deformation theory.
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.
This presentation of the neighborhoods of New Orleans offers an expert's perspective on the city's architectural diversity and details, one block at a time. New Orleans Times-Picayune columnist Stephanie Bruno presents the best of her "StreetWalker" column in this illustrated resource. From the Garden District to Mid-City, each block included features photographs of the homes, a description of the buildings, and a map for easy access.
The 1876 United States Centennial Exhibition in Philadelphia was not only the United States' first important world's fair, it signaled significant changes in the very shape of knowledge. Quarrels between participants in the exhibition represented a greater conflict as the world transitioned between two different kinds of modernity—the Enlightenment of the seventeenth and eighteenth centuries to the High Modern period of the nineteenth and twentieth centuries. At the center of this movement was a shift in the perceived relationship between seeing and knowing and in the perception of what makes an object valuable—its usefulness as a subject of study and learning versus its ability to be bought and sold on the market. Arguments over design of the Centennial reflected these opposing viewpoints. Initial plans were rigidly structured, dividing the exhibits by country and type. But as some exhibitors became more interested in the preferences of their audience, they adopted a more modern stance. Objects traditionally displayed in isolated glass boxes were placed in fictive context—the necklace draped over a mannequin, the vase set on a table in a model room. As a result, the audience could more easily perceive these items as commodities suitable for their own environments and the fair as a place to find ideas for a material lifestyle. Designing the Centennial is a vital first look at the design process and the nature of the display. Bruno Giberti uses official reports of the U.S. Centennial Commission and photographs of the Centennial Photographic Company, as well as the ephemera of the exhibition and literary accounts in books, magazines, and newspapers to illuminate how the 1876 fair revealed changes to come: in future world's fairs, museums, department stores, and in the nature of display itself.
A muckraking expose of corporate greenwashing and of the disturbing trend toward U.N.-corporate "partnerships" that give corporations good PR without requiring them to improve their behavior. In the decade between the Rio Earth Summit in 1992 and the Johannesburg World Summit on Sustainable Development in 2002, transnational corporations have increasingly used their resources to deter regulation, suppress opposing voices, and try to buy civil society's acquiescence with slick PR. But we don't have to acquiesce, and neither should the U.N. The United Nations may not be perfect, argue Kenny Bruno and Joshua Karliner, but in its principles and structure it has the potential to counter the WTO-a potential it is squandering, say the authors. earthsummit.biz exposes the current state of corporate rhetoric vs. corporate reality and debunks the paradigm of transnational "responsibility" and self-regulation. It contains 18 corporate case studies, as well as the complete texts of the U.N.'s toothless Global Compact with corporations, and the Global Compact's civil society counterpart, the Citizens Compact on the United Nations and Corporations.
Covering an exceptional range of topics, this text provides a unique overview of the Maurer—Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new conceptual treatment of the twisting procedure, guiding the reader through various versions with the help of plentiful motivating examples for graduate students as well as researchers. Topics covered include a novel approach to the twisting procedure for operads leading to Kontsevich graph homology and a description of the twisting procedure for (homotopy) associative algebras or (homotopy) Lie algebras using the biggest deformation gauge group ever considered. The book concludes with concise surveys of recent applications in areas including higher category theory and deformation theory.
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.
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