Lie Methods in Deformation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lie Methods in Deformation Theory write by Marco Manetti. This book was released on 2022-09-01. Lie Methods in Deformation Theory available in PDF, EPUB and Kindle. This book furnishes a comprehensive treatment of differential graded Lie algebras, L-infinity algebras, and their use in deformation theory. We believe it is the first textbook devoted to this subject, although the first chapters are also covered in other sources with a different perspective. Deformation theory is an important subject in algebra and algebraic geometry, with an origin that dates back to Kodaira, Spencer, Kuranishi, Gerstenhaber, and Grothendieck. In the last 30 years, a new approach, based on ideas from rational homotopy theory, has made it possible not only to solve long-standing open problems, but also to clarify the general theory and to relate apparently different features. This approach works over a field of characteristic 0, and the central role is played by the notions of differential graded Lie algebra, L-infinity algebra, and Maurer–Cartan equations. The book is written keeping in mind graduate students with a basic knowledge of homological algebra and complex algebraic geometry as utilized, for instance, in the book by K. Kodaira, Complex Manifolds and Deformation of Complex Structures. Although the main applications in this book concern deformation theory of complex manifolds, vector bundles, and holomorphic maps, the underlying algebraic theory also applies to a wider class of deformation problems, and it is a prerequisite for anyone interested in derived deformation theory. Researchers in algebra, algebraic geometry, algebraic topology, deformation theory, and noncommutative geometry are the major targets for the book.
Lie Methods in Deformation Theory
Lie Methods in Deformation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lie Methods in Deformation Theory write by Marco Manetti. This book was released on 2022-08-01. Lie Methods in Deformation Theory available in PDF, EPUB and Kindle. This book furnishes a comprehensive treatment of differential graded Lie algebras, L-infinity algebras, and their use in deformation theory. We believe it is the first textbook devoted to this subject, although the first chapters are also covered in other sources with a different perspective. Deformation theory is an important subject in algebra and algebraic geometry, with an origin that dates back to Kodaira, Spencer, Kuranishi, Gerstenhaber, and Grothendieck. In the last 30 years, a new approach, based on ideas from rational homotopy theory, has made it possible not only to solve long-standing open problems, but also to clarify the general theory and to relate apparently different features. This approach works over a field of characteristic 0, and the central role is played by the notions of differential graded Lie algebra, L-infinity algebra, and Maurer–Cartan equations. The book is written keeping in mind graduate students with a basic knowledge of homological algebra and complex algebraic geometry as utilized, for instance, in the book by K. Kodaira, Complex Manifolds and Deformation of Complex Structures. Although the main applications in this book concern deformation theory of complex manifolds, vector bundles, and holomorphic maps, the underlying algebraic theory also applies to a wider class of deformation problems, and it is a prerequisite for anyone interested in derived deformation theory. Researchers in algebra, algebraic geometry, algebraic topology, deformation theory, and noncommutative geometry are the major targets for the book.
Maurer–Cartan Methods in Deformation Theory
Maurer–Cartan Methods in Deformation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Maurer–Cartan Methods in Deformation Theory write by Vladimir Dotsenko. This book was released on 2023-08-31. Maurer–Cartan Methods in Deformation Theory available in PDF, EPUB and Kindle. 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.
Maurer–Cartan Methods in Deformation Theory
Maurer–Cartan Methods in Deformation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Maurer–Cartan Methods in Deformation Theory write by Vladimir Dotsenko. This book was released on 2023-08-31. Maurer–Cartan Methods in Deformation Theory available in PDF, EPUB and Kindle. 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.
Deformation Theory of Discontinuous Groups
Deformation Theory of Discontinuous Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Deformation Theory of Discontinuous Groups write by Ali Baklouti. This book was released on 2022-07-05. Deformation Theory of Discontinuous Groups available in PDF, EPUB and Kindle. This book contains the latest developments of the theory of discontinuous groups acting on homogenous spaces, from basic concepts to a comprehensive exposition. It develops the newest approaches and methods in the deformation theory of topological modules and unitary representations and focuses on the geometry of discontinuous groups of solvable Lie groups and their compact extensions. It also presents proofs of recent results, computes fundamental examples, and serves as an introduction and reference for students and experienced researchers in Lie theory, discontinuous groups, and deformation (and moduli) spaces.
