Lie Models In Topology
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Lie Models In Topology
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Author : Urtzi Buijs
language : en
Publisher: Springer Nature
Release Date : 2020-12-15
Lie Models In Topology written by Urtzi Buijs and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-15 with Mathematics categories.
Since the birth of rational homotopy theory, the possibility of extending the Quillen approach – in terms of Lie algebras – to a more general category of spaces, including the non-simply connected case, has been a challenge for the algebraic topologist community. Despite the clear Eckmann-Hilton duality between Quillen and Sullivan treatments, the simplicity in the realization of algebraic structures in the latter contrasts with the complexity required by the Lie algebra version. In this book, the authors develop new tools to address these problems. Working with complete Lie algebras, they construct, in a combinatorial way, a cosimplicial Lie model for the standard simplices. This is a key object, which allows the definition of a new model and realization functors that turn out to be homotopically equivalent to the classical Quillen functors in the simply connected case. With this, the authors open new avenues for solving old problems and posing new questions. This monograph is the winner of the 2020 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics.
Algebraic Models In Geometry
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Author : Yves Félix
language : en
Publisher: Oxford University Press
Release Date : 2008
Algebraic Models In Geometry written by Yves Félix and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
A text aimed at both geometers needing the tools of rational homotopy theory to understand and discover new results concerning various geometric subjects, and topologists who require greater breadth of knowledge about geometric applications of the algebra of homotopy theory.
Lie Algebras Of Finite And Affine Type
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Author : Roger William Carter
language : en
Publisher: Cambridge University Press
Release Date : 2005-10-27
Lie Algebras Of Finite And Affine Type written by Roger William Carter and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-27 with Mathematics categories.
This book provides a thorough but relaxed mathematical treatment of Lie algebras.
Cutting Edge Mathematics
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Author : Henar Herrero
language : en
Publisher: Springer Nature
Release Date : 2024-08-25
Cutting Edge Mathematics written by Henar Herrero and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-25 with Mathematics categories.
The book contains a selection of research and expository papers in pure and applied mathematics presented by various authors as plenary or invited speakers at the biennial congress of the Spanish Royal Mathematical Society held in Ciudad Real (Spain) in January 2022. The main results focus on the Yang problem and its solution proposed by Globevnik; a phylogenetic reconstruction based on algebra; the Calderon problem for local and nonlocal Schrödinger equations; some open problems in orthogonal polynomial theory; Quillen’s rational homotopy theory; Ulrich bundles and applications; and free objects in theory of Banach spaces. Researchers in these fields are potential audiences.
Geometry Of Lie Groups
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Author : B. Rosenfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-02-28
Geometry Of Lie Groups written by B. Rosenfeld and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-28 with Mathematics categories.
This book is the result of many years of research in Non-Euclidean Geometries and Geometry of Lie groups, as well as teaching at Moscow State University (1947- 1949), Azerbaijan State University (Baku) (1950-1955), Kolomna Pedagogical Col lege (1955-1970), Moscow Pedagogical University (1971-1990), and Pennsylvania State University (1990-1995). My first books on Non-Euclidean Geometries and Geometry of Lie groups were written in Russian and published in Moscow: Non-Euclidean Geometries (1955) [Ro1] , Multidimensional Spaces (1966) [Ro2] , and Non-Euclidean Spaces (1969) [Ro3]. In [Ro1] I considered non-Euclidean geometries in the broad sense, as geometry of simple Lie groups, since classical non-Euclidean geometries, hyperbolic and elliptic, are geometries of simple Lie groups of classes Bn and D , and geometries of complex n and quaternionic Hermitian elliptic and hyperbolic spaces are geometries of simple Lie groups of classes An and en. [Ro1] contains an exposition of the geometry of classical real non-Euclidean spaces and their interpretations as hyperspheres with identified antipodal points in Euclidean or pseudo-Euclidean spaces, and in projective and conformal spaces. Numerous interpretations of various spaces different from our usual space allow us, like stereoscopic vision, to see many traits of these spaces absent in the usual space.
Hilbert S Fifth Problem And Related Topics
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Author : Terence Tao
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-07-18
Hilbert S Fifth Problem And Related Topics written by Terence Tao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-18 with Mathematics categories.
In the fifth of his famous list of 23 problems, Hilbert asked if every topological group which was locally Euclidean was in fact a Lie group. Through the work of Gleason, Montgomery-Zippin, Yamabe, and others, this question was solved affirmatively; more generally, a satisfactory description of the (mesoscopic) structure of locally compact groups was established. Subsequently, this structure theory was used to prove Gromov's theorem on groups of polynomial growth, and more recently in the work of Hrushovski, Breuillard, Green, and the author on the structure of approximate groups. In this graduate text, all of this material is presented in a unified manner, starting with the analytic structural theory of real Lie groups and Lie algebras (emphasising the role of one-parameter groups and the Baker-Campbell-Hausdorff formula), then presenting a proof of the Gleason-Yamabe structure theorem for locally compact groups (emphasising the role of Gleason metrics), from which the solution to Hilbert's fifth problem follows as a corollary. After reviewing some model-theoretic preliminaries (most notably the theory of ultraproducts), the combinatorial applications of the Gleason-Yamabe theorem to approximate groups and groups of polynomial growth are then given. A large number of relevant exercises and other supplementary material are also provided.
A Concise Course In Algebraic Topology
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Author : J. P. May
language : en
Publisher: University of Chicago Press
Release Date : 1999-09
A Concise Course In Algebraic Topology written by J. P. May and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09 with Mathematics categories.
Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
Basic Lie Theory
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Author : Hossein Abbaspour
language : en
Publisher: World Scientific
Release Date : 2007
Basic Lie Theory written by Hossein Abbaspour and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Science categories.
This volume provides a comprehensive treatment of basic Lie theory, primarily directed toward graduate study. The text is ideal for a full graduate course in Lie groups and Lie algebras. However, the book is also very usable for a variety of other courses: a one-semester course in Lie algebras, or on Haar measure and its applications, for advanced undergraduates; or as the text for one-semester graduate courses in Lie groups and symmetric spaces of non-compact type, or in lattices in Lie groups. The material is complete and detailed enough to be used for self-study; it can also serve as a reference work for professional mathematicians working in other areas. The book's utility for such a varied readership is enhanced by a diagram showing the interdependence of the separate chapters so that individual chapters and the material they depend upon can be selected, while others can be skipped.The book incorporates many of the most significant discoveries and pioneering contributions of the masters of the subject: Borel, Cartan, Chevalley, Iwasawa, Mostow, Siegel, and Weyl, among others.
Exotic Smoothness And Physics Differential Topology And Spacetime Models
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Author : Torsten Asselmeyer-maluga
language : en
Publisher: World Scientific
Release Date : 2007-01-23
Exotic Smoothness And Physics Differential Topology And Spacetime Models written by Torsten Asselmeyer-maluga and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-23 with Science categories.
The recent revolution in differential topology related to the discovery of non-standard (”exotic”) smoothness structures on topologically trivial manifolds such as R4 suggests many exciting opportunities for applications of potentially deep importance for the spacetime models of theoretical physics, especially general relativity. This rich panoply of new differentiable structures lies in the previously unexplored region between topology and geometry. Just as physical geometry was thought to be trivial before Einstein, physicists have continued to work under the tacit — but now shown to be incorrect — assumption that differentiability is uniquely determined by topology for simple four-manifolds. Since diffeomorphisms are the mathematical models for physical coordinate transformations, Einstein's relativity principle requires that these models be physically inequivalent. This book provides an introductory survey of some of the relevant mathematics and presents preliminary results and suggestions for further applications to spacetime models.
Higher Structures And Operadic Calculus
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Author : Bruno Vallette
language : en
Publisher: Springer Nature
Release Date : 2025-05-19
Higher Structures And Operadic Calculus written by Bruno Vallette and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-19 with Mathematics categories.
This book presents the notes originating from five series of lectures given at the CRM Barcelona in 21-25 June, 2021, during the “Higher homotopical structures” programme. Since their introduction 60 years ago, the notions of infinity algebras (Stasheff, Sugawara), higher categories (Boardman-Vogt), operads (May), and model categories (Quillen) have given rise to powerful new tools which made possible the resolution of open problems and prompted revolutions in many domains like algebraic topology (rational homotopy theory, faithful algebraic invariants of the homotopy type of spaces), deformation theory (formality theorems, formal moduli problems), and mathematical physics (quantization of Poisson manifolds, quantum field theories), to name but a few. This theory of higher structures using operadic calculus is currently under rapid development. The aim of this book is to provide the community with an accessible state-of-the-art, while at the same time giving interested researchers and advanced students a brief overview on the subject.