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Author : Richard S. Palais
Publisher : American Mathematical Soc.
ISBN 13 : 082181236X
Total Pages : 81 pages
Book Rating : 4.8/5 (218 download)
Download or read book The Classification of $G$-Spaces written by Richard S. Palais and published by American Mathematical Soc.. This book was released on 1960 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Su Gao
Publisher : American Mathematical Soc.
ISBN 13 : 0821831909
Total Pages : 78 pages
Book Rating : 4.8/5 (218 download)
Download or read book On the Classification of Polish Metric Spaces Up to Isometry written by Su Gao and published by American Mathematical Soc.. This book was released on 2003 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Shmuel Weinberger
Publisher : University of Chicago Press
ISBN 13 : 9780226885667
Total Pages : 314 pages
Book Rating : 4.8/5 (856 download)
Download or read book The Topological Classification of Stratified Spaces written by Shmuel Weinberger and published by University of Chicago Press. This book was released on 1994 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the theory for stratified spaces, along with important examples and applications, that is analogous to the surgery theory for manifolds. In the first expository account of this field, Weinberger provides topologists with a new way of looking at the classification theory of singular spaces with his original results. Divided into three parts, the book begins with an overview of modern high-dimensional manifold theory. Rather than including complete proofs of all theorems, Weinberger demonstrates key constructions, gives convenient formulations, and shows the usefulness of the technology. Part II offers the parallel theory for stratified spaces. Here, the topological category is most completely developed using the methods of "controlled topology." Many examples illustrating the topological invariance and noninvariance of obstructions and characteristic classes are provided. Applications for embeddings and immersions of manifolds, for the geometry of group actions, for algebraic varieties, and for rigidity theorems are found in Part III. This volume will be of interest to topologists, as well as mathematicians in other fields such as differential geometry, operator theory, and algebraic geometry.
Author : Shmuel Weinberger
Publisher : University of Chicago Press
ISBN 13 : 9780226885674
Total Pages : 308 pages
Book Rating : 4.8/5 (856 download)
Download or read book The Topological Classification of Stratified Spaces written by Shmuel Weinberger and published by University of Chicago Press. This book was released on 1994 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the theory for stratified spaces, along with important examples and applications, that is analogous to the surgery theory for manifolds. In the first expository account of this field, Weinberger provides topologists with a new way of looking at the classification theory of singular spaces with his original results. Divided into three parts, the book begins with an overview of modern high-dimensional manifold theory. Rather than including complete proofs of all theorems, Weinberger demonstrates key constructions, gives convenient formulations, and shows the usefulness of the technology. Part II offers the parallel theory for stratified spaces. Here, the topological category is most completely developed using the methods of "controlled topology." Many examples illustrating the topological invariance and noninvariance of obstructions and characteristic classes are provided. Applications for embeddings and immersions of manifolds, for the geometry of group actions, for algebraic varieties, and for rigidity theorems are found in Part III. This volume will be of interest to topologists, as well as mathematicians in other fields such as differential geometry, operator theory, and algebraic geometry.
Author : Kaspar Riesen
Publisher : World Scientific
ISBN 13 : 9814465038
Total Pages : 346 pages
Book Rating : 4.8/5 (144 download)
Download or read book Graph Classification And Clustering Based On Vector Space Embedding written by Kaspar Riesen and published by World Scientific. This book was released on 2010-04-29 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with a fundamentally novel approach to graph-based pattern recognition based on vector space embedding of graphs. It aims at condensing the high representational power of graphs into a computationally efficient and mathematically convenient feature vector.This volume utilizes the dissimilarity space representation originally proposed by Duin and Pekalska to embed graphs in real vector spaces. Such an embedding gives one access to all algorithms developed in the past for feature vectors, which has been the predominant representation formalism in pattern recognition and related areas for a long time.
Author : Kyung Bai Lee
Publisher : American Mathematical Soc.
ISBN 13 : 0821852310
Total Pages : 418 pages
Book Rating : 4.8/5 (218 download)
Download or read book Seifert Fiberings written by Kyung Bai Lee and published by American Mathematical Soc.. This book was released on 2010-11-24 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seifert fiberings extend the notion of fiber bundle mappings by allowing some of the fibers to be singular. Away from the singular fibers, the fibering is an ordinary bundle with fiber a fixed homogeneous space. The singular fibers are quotients of this homogeneous space by distinguished groups of homeomorphisms. These fiberings are ubiquitous and important in mathematics. This book describes in a unified way their structure, how they arise, and how they are classified and used in applications. Manifolds possessing such fiber structures are discussed and range from the classical three-dimensional Seifert manifolds to higher dimensional analogues encompassing, for example, flat manifolds, infra-nil-manifolds, space forms, and their moduli spaces. The necessary tools not covered in basic graduate courses are treated in considerable detail. These include transformation groups, cohomology of groups, and needed Lie theory. Inclusion of the Bieberbach theorems, existence, uniqueness, and rigidity of Seifert fiberings, aspherical manifolds, symmetric spaces, toral rank of spherical space forms, equivariant cohomology, polynomial structures on solv-manifolds, fixed point theory, and other examples, exercises and applications attest to the breadth of these fiberings. This is the first time the scattered literature on singular fiberings is brought together in a unified approach. The new methods and tools employed should be valuable to researchers and students interested in geometry and topology.
Author : Maurice J. Dupré
Publisher : American Mathematical Soc.
ISBN 13 : 0821822225
Total Pages : 77 pages
Book Rating : 4.8/5 (218 download)
Download or read book The Classification and Structure of C^*-Algebra Bundles written by Maurice J. Dupré and published by American Mathematical Soc.. This book was released on 1979 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michel Cahen
Publisher : American Mathematical Soc.
ISBN 13 : 0821822292
Total Pages : 108 pages
Book Rating : 4.8/5 (218 download)
Download or read book Pseudo-Riemannian Symmetric Spaces written by Michel Cahen and published by American Mathematical Soc.. This book was released on 1980 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Carlo Alabiso
Publisher : Springer Nature
ISBN 13 : 3030674177
Total Pages : 343 pages
Book Rating : 4.0/5 (36 download)
Download or read book A Primer on Hilbert Space Theory written by Carlo Alabiso and published by Springer Nature. This book was released on 2021-03-03 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an essential introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for providing an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, lies in the strenuous mathematics demands that even the simplest physical cases entail. Graduate courses in physics rarely offer enough time to cover the theory of Hilbert space and operators, as well as distribution theory, with sufficient mathematical rigor. Accordingly, compromises must be found between full rigor and the practical use of the instruments. Based on one of the authors’s lectures on functional analysis for graduate students in physics, the book will equip readers to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. It also includes a brief introduction to topological groups, and to other mathematical structures akin to Hilbert space. Exercises and solved problems accompany the main text, offering readers opportunities to deepen their understanding. The topics and their presentation have been chosen with the goal of quickly, yet rigorously and effectively, preparing readers for the intricacies of Hilbert space. Consequently, some topics, e.g., the Lebesgue integral, are treated in a somewhat unorthodox manner. The book is ideally suited for use in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.
Author : J. Peter May
Publisher : American Mathematical Soc.
ISBN 13 : 0821818554
Total Pages : 116 pages
Book Rating : 4.8/5 (218 download)
Download or read book Classifying Spaces and Fibrations written by J. Peter May and published by American Mathematical Soc.. This book was released on 1975 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basic theory of fibrations is generalized to a context in which fibres, and maps on fibres, are constrained to lie in any preassigned category of spaces [script capital] F. Then axioms are placed on [script capital] F to allow the development of a theory of associated principal fibrations and, under several choices of additional hypotheses on [script capital] F, a classification theorem is proven for such fibrations.
Author : Jörg Feldvoss
Publisher : Springer
ISBN 13 : 3030115216
Total Pages : 322 pages
Book Rating : 4.0/5 (31 download)
Download or read book Advances in Algebra written by Jörg Feldvoss and published by Springer. This book was released on 2019-02-27 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume covers a range of research topics in algebra from the Southern Regional Algebra Conference (SRAC) that took place in March 2017. Presenting theory as well as computational methods, featured survey articles and research papers focus on ongoing research in algebraic geometry, ring theory, group theory, and associative algebras. Topics include algebraic groups, combinatorial commutative algebra, computational methods for representations of groups and algebras, group theory, Hopf-Galois theory, hypergroups, Lie superalgebras, matrix analysis, spherical and algebraic spaces, and tropical algebraic geometry. Since 1988, SRAC has been an important event for the algebra research community in the Gulf Coast Region and surrounding states, building a strong network of algebraists that fosters collaboration in research and education. This volume is suitable for graduate students and researchers interested in recent findings in computational and theoretical methods in algebra and representation theory.
Author : Burt Totaro
Publisher : Cambridge University Press
ISBN 13 : 113991605X
Total Pages : 245 pages
Book Rating : 4.1/5 (399 download)
Download or read book Group Cohomology and Algebraic Cycles written by Burt Totaro and published by Cambridge University Press. This book was released on 2014-06-26 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group cohomology reveals a deep relationship between algebra and topology, and its recent applications have provided important insights into the Hodge conjecture and algebraic geometry more broadly. This book presents a coherent suite of computational tools for the study of group cohomology and algebraic cycles. Early chapters synthesize background material from topology, algebraic geometry, and commutative algebra so readers do not have to form connections between the literatures on their own. Later chapters demonstrate Peter Symonds's influential proof of David Benson's regularity conjecture, offering several new variants and improvements. Complete with concrete examples and computations throughout, and a list of open problems for further study, this book will be valuable to graduate students and researchers in algebraic geometry and related fields.
Author : Anthony Bak
Publisher : Springer Science & Business Media
ISBN 13 : 9781402007835
Total Pages : 272 pages
Book Rating : 4.0/5 (78 download)
Download or read book Current Trends in Transformation Groups written by Anthony Bak and published by Springer Science & Business Media. This book was released on 2002-07-31 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of some of the most active topics in the theory of transformation groups over the past decades and stresses advances obtained in the last dozen years. The emphasis is on actions of Lie groups on manifolds and CW complexes. Manifolds and actions of Lie groups on them are studied in the linear, semialgebraic, definable, analytic, smooth, and topological categories. Equivalent vector bundles play an important role. The work is divided into fifteen articles and will be of interest to anyone researching or studying transformations groups. The references make it easy to find details and original accounts of the topics surveyed, including tools and theories used in these accounts.
Author :
Publisher :
ISBN 13 :
Total Pages : 680 pages
Book Rating : 4.F/5 ( download)
Download or read book Annals of Mathematics written by and published by . This book was released on 1961 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: Founded in 1884, Annals of Mathematics publishes research papers in pure mathematics.
Author : J. P. May
Publisher : University of Chicago Press
ISBN 13 : 9780226511832
Total Pages : 262 pages
Book Rating : 4.5/5 (118 download)
Download or read book A Concise Course in Algebraic Topology written by J. P. May and published by University of Chicago Press. This book was released on 1999-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Jörg Winkelmann
Publisher : Springer
ISBN 13 : 3540491856
Total Pages : 243 pages
Book Rating : 4.5/5 (44 download)
Download or read book The Classification of Three-dimensional Homogeneous Complex Manifolds written by Jörg Winkelmann and published by Springer. This book was released on 2006-11-14 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a classification of all three-dimensional complex manifolds for which there exists a transitive action (by biholomorphic transformations) of a real Lie group. This means two homogeneous complex manifolds are considered equivalent if they are isomorphic as complex manifolds. The classification is based on methods from Lie group theory, complex analysis and algebraic geometry. Basic knowledge in these areas is presupposed.
Author : Sigurdur Helgason
Publisher : American Mathematical Soc.
ISBN 13 : 0821828487
Total Pages : 682 pages
Book Rating : 4.8/5 (218 download)
Download or read book Differential Geometry, Lie Groups, and Symmetric Spaces written by Sigurdur Helgason and published by American Mathematical Soc.. This book was released on 2001-06-12 with total page 682 pages. Available in PDF, EPUB and Kindle. Book excerpt: A great book ... a necessary item in any mathematical library. --S. S. Chern, University of California A brilliant book: rigorous, tightly organized, and covering a vast amount of good mathematics. --Barrett O'Neill, University of California This is obviously a very valuable and well thought-out book on an important subject. --Andre Weil, Institute for Advanced Study The study of homogeneous spaces provides excellent insights into both differential geometry and Lie groups. In geometry, for instance, general theorems and properties will also hold for homogeneous spaces, and will usually be easier to understand and to prove in this setting. For Lie groups, a significant amount of analysis either begins with or reduces to analysis on homogeneous spaces, frequently on symmetric spaces. For many years and for many mathematicians, Sigurdur Helgason's classic Differential Geometry, Lie Groups, and Symmetric Spaces has been--and continues to be--the standard source for this material. Helgason begins with a concise, self-contained introduction to differential geometry. Next is a careful treatment of the foundations of the theory of Lie groups, presented in a manner that since 1962 has served as a model to a number of subsequent authors. This sets the stage for the introduction and study of symmetric spaces, which form the central part of the book. The text concludes with the classification of symmetric spaces by means of the Killing-Cartan classification of simple Lie algebras over $\mathbb{C}$ and Cartan's classification of simple Lie algebras over $\mathbb{R}$, following a method of Victor Kac. The excellent exposition is supplemented by extensive collections of useful exercises at the end of each chapter. All of the problems have either solutions or substantial hints, found at the back of the book. For this edition, the author has made corrections and added helpful notes and useful references. Sigurdur Helgason was awarded the Steele Prize for Differential Geometry, Lie Groups, and Symmetric Spaces and Groups and Geometric Analysis.
