Three-dimensional geometry and topology, Thurston, William P.

Автор: Kauffman L. H., Manturov V. O.
Название: New Ideas in Low Dimensional Topology
ISBN: 9814630616 ISBN-13(EAN): 9789814630610
Издательство: World Scientific Publishing
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Описание: This Book Consists Of A Selection Of Articles Devoted To New Ideas And Develpments In Low Dimensional Topology. Low Dimensions Refer To Dimensions Three And Four For The Topology Of Manifolds And Their Submanifolds. Thus We Have Papers Related To Both Manifolds And To Knotted Submanifolds Of Dimension One In Three (Classical Knot Theory) And Two In Four (Surfaces In Four Dimensional Spaces). Some Of The Work Involves Virtual Knot Theory Where The Knots Are Abstractions Of Classical Knots But Can Be Represented By Knots Embedded In Surfaces. This Leads Both To New Interactions With Classical Topology And To New Interactions With Essential Combinatorics.

Автор: Naber
Название: Topology, Geometry and Gauge fields
ISBN: 1441972536 ISBN-13(EAN): 9781441972538
Издательство: Springer
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Описание: This is a book on topology and geometry and, like any books on subjects as vast as these, it has a point-of-view that guided the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. We ask the reader to come to us with some vague notion of what an electromagnetic field might be, a willingness to accept a few of the more elementary pronouncements of quantum mechanics, a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. To such a reader we offer an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1. Iwould go over both volumes thoroughly and make some minor changes in terminology and notation and correct any errors I find. In this new edition, a chapter on Singular Homology will be added as well as minor changes in notation and terminology throughout and some sections have been rewritten or omitted. Reviews of First Edition: “It is unusual to find a book so carefully tailored to the needs of this interdisciplinary area of mathematical physics...Naber combines a knowledge of his subject with an excellent informal writing style. (NZMS Newletter) ...this book should be very interesting for mathematicians and physicists (as well as other scientists) who are concerned with gauge theories. (Zentralblatt Fuer Mathematik)