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Author: Mary-Elizabeth Hamstrom
Publisher: American Mathematical Soc.
ISBN: 0821812408
Category : Conformal mapping
Languages : en
Pages : 47
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Book Description
Author: Mary-Elizabeth Hamstrom
Publisher: American Mathematical Soc.
ISBN: 0821812408
Category : Conformal mapping
Languages : en
Pages : 47
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Book Description
Author: Marion Kirkland Fort
Publisher:
ISBN:
Category : Algebraic topology
Languages : en
Pages : 280
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Book Description
Author: Vladimir G. Turaev
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110434563
Category : Mathematics
Languages : en
Pages : 620
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Book Description
Due to the strong appeal and wide use of this monograph, it is now available in its third revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups. The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space. This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. Contents: Invariants of graphs in Euclidean 3-space and of closed 3-manifolds Foundations of topological quantum field theory Three-dimensional topological quantum field theory Two-dimensional modular functors 6j-symbols Simplicial state sums on 3-manifolds Shadows of manifolds and state sums on shadows Constructions of modular categories
Author: K. Johannson
Publisher: Springer
ISBN: 3540384863
Category : Mathematics
Languages : en
Pages : 312
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Book Description
Author:
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 862
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Book Description
Without specializing in a small number of subject areas, this journal emphasizes the most active and influential areas of current mathematics.
Author: Renzo A. Piccinini
Publisher: Springer
ISBN: 3540470913
Category : Mathematics
Languages : en
Pages : 223
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Book Description
Since the subject of Groups of Self-Equivalences was first discussed in 1958 in a paper of Barcuss and Barratt, a good deal of progress has been achieved. This is reviewed in this volume, first by a long survey article and a presentation of 17 open problems together with a bibliography of the subject, and by a further 14 original research articles.
Author: R. H. Bing
Publisher: Princeton University Press
ISBN: 1400882079
Category : Mathematics
Languages : en
Pages : 256
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Book Description
During the summer of 1965, an informal seminar in geometric topology was held at the University of Wisconsin under the direction of Professor Bing. Twenty-five of these lectures are included in this study, among them Professor Bing's lecture describing the recent attacks of Haken and Poincaré on the Poincaré conjectures, and sketching a proof of Haken's main result.
Author: Viacheslav Z. Grines
Publisher: Springer
ISBN: 3319448471
Category : Mathematics
Languages : en
Pages : 314
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Book Description
This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A. The main results on the topological classification of discrete dynamical systems are widely scattered among many papers and surveys. This book presents these results fluidly, systematically, and for the first time in one publication. Additionally, this book discusses the recent results on the topological classification of Axiom A diffeomorphisms focusing on the nontrivial effects of the dynamical systems on 2- and 3-manifolds. The classical methods and approaches which are considered to be promising for the further research are also discussed.“br> The reader needs to be familiar with the basic concepts of the qualitative theory of dynamical systems which are presented in Part 1 for convenience. The book is accessible to ambitious undergraduates, graduates, and researchers in dynamical systems and low dimensional topology. This volume consists of 10 chapters; each chapter contains its own set of references and a section on further reading. Proofs are presented with the exact statements of the results. In Chapter 10 the authors briefly state the necessary definitions and results from algebra, geometry and topology. When stating ancillary results at the beginning of each part, the authors refer to other sources which are readily available.
Author:
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 774
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Book Description
Author: Library of Congress. Copyright Office
Publisher: Copyright Office, Library of Congress
ISBN:
Category : Copyright
Languages : en
Pages : 1052
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Book Description
Includes Part 1, Number 2: Books and Pamphlets, Including Serials and Contributions to Periodicals July - December)
