Download or read book Continuous Cohomology of the Lie Algebra of Vector Fields written by Tōru Tsujishita and published by American Mathematical Soc.. This book was released on 1981 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper collects notations, definitions and facts about distributions, differential graded algebras, continuous cohomology of topological Lie algebras, etc. and state the main results. We then recall the results of Guillemin-Losik, Losik and Haefliger, rewriting them in a form suitable for proving them in somewhat different ways from the original proofs. We prove the main theorems, and the theorem from part one.
Download or read book Introduction to Smooth Manifolds written by John M. Lee and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why
Download or read book An Introduction to Manifolds written by Loring W. Tu and published by Springer Science & Business Media. This book was released on 2010-10-05 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Download or read book Foliations on Riemannian Manifolds written by Philippe Tondeur and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: A first approximation to the idea of a foliation is a dynamical system, and the resulting decomposition of a domain by its trajectories. This is an idea that dates back to the beginning of the theory of differential equations, i.e. the seventeenth century. Towards the end of the nineteenth century, Poincare developed methods for the study of global, qualitative properties of solutions of dynamical systems in situations where explicit solution methods had failed: He discovered that the study of the geometry of the space of trajectories of a dynamical system reveals complex phenomena. He emphasized the qualitative nature of these phenomena, thereby giving strong impetus to topological methods. A second approximation is the idea of a foliation as a decomposition of a manifold into submanifolds, all being of the same dimension. Here the presence of singular submanifolds, corresponding to the singularities in the case of a dynamical system, is excluded. This is the case we treat in this text, but it is by no means a comprehensive analysis. On the contrary, many situations in mathematical physics most definitely require singular foliations for a proper modeling. The global study of foliations in the spirit of Poincare was begun only in the 1940's, by Ehresmann and Reeb.
Download or read book An Introduction to Lie Groups and Lie Algebras written by Alexander A. Kirillov and published by Cambridge University Press. This book was released on 2008-07-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.
Download or read book Journal of Nonlinear Mathematical Physics Vol 14 written by and published by atlantis press. This book was released on with total page 647 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Crossed Modules written by Friedrich Wagemann and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-10-25 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents material in two parts. Part one provides an introduction to crossed modules of groups, Lie algebras and associative algebras with fully written out proofs and is suitable for graduate students interested in homological algebra. In part two, more advanced and less standard topics such as crossed modules of Hopf algebra, Lie groups, and racks are discussed as well as recent developments and research on crossed modules.
Download or read book Differential Geometry of Foliations written by B.L. Reinhart and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Whoever you are! How can I but offer you divine leaves . . . ? Walt Whitman The object of study in modern differential geometry is a manifold with a differ ential structure, and usually some additional structure as well. Thus, one is given a topological space M and a family of homeomorphisms, called coordinate sys tems, between open subsets of the space and open subsets of a real vector space V. It is supposed that where two domains overlap, the images are related by a diffeomorphism, called a coordinate transformation, between open subsets of V. M has associated with it a tangent bundle, which is a vector bundle with fiber V and group the general linear group GL(V). The additional structures that occur include Riemannian metrics, connections, complex structures, foliations, and many more. Frequently there is associated to the structure a reduction of the group of the tangent bundle to some subgroup G of GL(V). It is particularly pleasant if one can choose the coordinate systems so that the Jacobian matrices of the coordinate transformations belong to G. A reduction to G is called a G-structure, which is called integrable (or flat) if the condition on the Jacobians is satisfied. The strength of the integrability hypothesis is well-illustrated by the case of the orthogonal group On. An On-structure is given by the choice of a Riemannian metric, and therefore exists on every smooth manifold.
Download or read book Continuous Cohomology of Spaces with Two Topologies written by Mark Alan Mostow and published by American Mathematical Soc.. This book was released on 1976 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper investigates the continuous cohomology of spaces with two topologies. The present paper studies other possible definitions of continuous cohomology and compares them by computing examples and by introducing four axioms which are shown to characterize the continuous cohomology of a foliated manifold (with its ordinary and leaf topologies).
Download or read book Continuous Cohomology Discrete Subgroups and Representations of Reductive Groups written by Armand Borel and published by American Mathematical Soc.. This book was released on 2013-11-21 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been nearly twenty years since the first edition of this work. In the intervening years, there has been immense progress in the use of homological algebra to construct admissible representations and in the study of arithmetic groups. This second edition is a corrected and expanded version of the original, which was an important catalyst in the expansion of the field. Besides the fundamental material on cohomology and discrete subgroups present in the first edition, this edition also contains expositions of some of the most important developments of the last two decades.
Download or read book Cohomology of Infinite Dimensional Lie Algebras written by D.B. Fuks and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is no question that the cohomology of infinite dimensional Lie algebras deserves a brief and separate mono graph. This subject is not cover~d by any of the tradition al branches of mathematics and is characterized by relative ly elementary proofs and varied application. Moreover, the subject matter is widely scattered in various research papers or exists only in verbal form. The theory of infinite-dimensional Lie algebras differs markedly from the theory of finite-dimensional Lie algebras in that the latter possesses powerful classification theo rems, which usually allow one to "recognize" any finite dimensional Lie algebra (over the field of complex or real numbers), i.e., find it in some list. There are classifica tion theorems in the theory of infinite-dimensional Lie al gebras as well, but they are encumbered by strong restric tions of a technical character. These theorems are useful mainly because they yield a considerable supply of interest ing examples. We begin with a list of such examples, and further direct our main efforts to their study.
Download or read book Cohomology of Infinite Dimensional Lie Algebras written by D B Fuks and published by . This book was released on 1986-12-31 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Manifolds Tokyo 1973 written by Akio Hattori and published by University of Tokyo Press. This book was released on 1975 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Encyclopedic Dictionary of Mathematics written by Nihon Sūgakkai and published by MIT Press. This book was released on 1993 with total page 1180 pages. Available in PDF, EPUB and Kindle. Book excerpt: V.1. A.N. v.2. O.Z. Apendices and indexes.
Download or read book Real Homotopy of Configuration Spaces written by Najib Idrissi and published by Springer Nature. This book was released on 2022-06-11 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a unified and accessible account of recent developments regarding the real homotopy type of configuration spaces of manifolds. Configuration spaces consist of collections of pairwise distinct points in a given manifold, the study of which is a classical topic in algebraic topology. One of this theory’s most important questions concerns homotopy invariance: if a manifold can be continuously deformed into another one, then can the configuration spaces of the first manifold be continuously deformed into the configuration spaces of the second? This conjecture remains open for simply connected closed manifolds. Here, it is proved in characteristic zero (i.e. restricted to algebrotopological invariants with real coefficients), using ideas from the theory of operads. A generalization to manifolds with boundary is then considered. Based on the work of Campos, Ducoulombier, Lambrechts, Willwacher, and the author, the book covers a vast array of topics, including rational homotopy theory, compactifications, PA forms, propagators, Kontsevich integrals, and graph complexes, and will be of interest to a wide audience.
Download or read book Algebraic Models in Geometry written by Yves Félix and published by Oxford University Press. This book was released on 2008 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Smooth Manifolds written by John Lee and published by Springer Science & Business Media. This book was released on 2012-08-27 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research--- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer. This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier so that they can be used throughout the book. A few new topics have been added, notably Sard’s theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of first-order partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures. Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.
