Topology And Geometry In Dimension Three

Author : E.E. Moise
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 55,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781461299066

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Geometric Topology in Dimensions 2 and 3 by E.E. Moise Pdf

Geometric topology may roughly be described as the branch of the topology of manifolds which deals with questions of the existence of homeomorphisms. Only in fairly recent years has this sort of topology achieved a sufficiently high development to be given a name, but its beginnings are easy to identify. The first classic result was the SchOnflies theorem (1910), which asserts that every 1-sphere in the plane is the boundary of a 2-cell. In the next few decades, the most notable affirmative results were the "Schonflies theorem" for polyhedral 2-spheres in space, proved by J. W. Alexander [Ad, and the triangulation theorem for 2-manifolds, proved by T. Rad6 [Rd. But the most striking results of the 1920s were negative. In 1921 Louis Antoine [A ] published an extraordinary paper in which he 4 showed that a variety of plausible conjectures in the topology of 3-space were false. Thus, a (topological) Cantor set in 3-space need not have a simply connected complement; therefore a Cantor set can be imbedded in 3-space in at least two essentially different ways; a topological 2-sphere in 3-space need not be the boundary of a 3-cell; given two disjoint 2-spheres in 3-space, there is not necessarily any third 2-sphere which separates them from one another in 3-space; and so on and on. The well-known "horned sphere" of Alexander [A ] appeared soon thereafter.

Author : William P. Thurston
Publisher : Princeton University Press
Page : 323 pages
File Size : 53,5 Mb
Release : 2014-10-31
Category : Mathematics
ISBN : 9781400865321

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Three-Dimensional Geometry and Topology, Volume 1 by William P. Thurston Pdf

This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty. This book was the origin of a grand scheme developed by Thurston that is now coming to fruition. In the 1920s and 1930s the mathematics of two-dimensional spaces was formalized. It was Thurston's goal to do the same for three-dimensional spaces. To do this, he had to establish the strong connection of geometry to topology--the study of qualitative questions about geometrical structures. The author created a new set of concepts, and the expression "Thurston-type geometry" has become a commonplace. Three-Dimensional Geometry and Topology had its origins in the form of notes for a graduate course the author taught at Princeton University between 1978 and 1980. Thurston shared his notes, duplicating and sending them to whoever requested them. Eventually, the mailing list grew to more than one thousand names. The book is the culmination of two decades of research and has become the most important and influential text in the field. Its content also provided the methods needed to solve one of mathematics' oldest unsolved problems--the Poincaré Conjecture. In 2005 Thurston won the first AMS Book Prize, for Three-dimensional Geometry and Topology. The prize recognizes an outstanding research book that makes a seminal contribution to the research literature. Thurston received the Fields Medal, the mathematical equivalent of the Nobel Prize, in 1982 for the depth and originality of his contributions to mathematics. In 1979 he was awarded the Alan T. Waterman Award, which recognizes an outstanding young researcher in any field of science or engineering supported by the National Science Foundation.

Author : Weiping Li
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 40,9 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852958

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Topology and Geometry in Dimension Three by Weiping Li Pdf

This volume contains the proceedings of a conference held from June 4-6, 2010, at Oklahoma State University, in honor of William (Bus) Jaco's 70th birthday. His contributions to research in low dimensional geometry and topology and to the American mathematical community, especially through his work for the American Mathematical Society, were recognized during the conference. The focus of the conference was on triangulations and geometric structures for three-dimensional manifolds. The papers in this volume present significant new results on these topics, as well as in geometric group theory.

Author : Weiping Li
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 42,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821889787

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Topology and Geometry in Dimension Three by Weiping Li Pdf

This volume contains the proceedings of a conference held from June 4-6, 2010, at Oklahoma State University, in honor of William (Bus) Jaco's 70th birthday. His contributions to research in low dimensional geometry and topology and to the American mathematical community, especially through his work for the American Mathematical Society, were recognized during the conference. The focus of the conference was on triangulations and geometric structures for three-dimensional manifolds. The papers in this volume present significant new results on these topics, as well as in geometric group theory.

Author : William P. Thurston
Publisher : American Mathematical Society
Page : 337 pages
File Size : 41,8 Mb
Release : 2023-06-16
Category : Mathematics
ISBN : 9781470474744

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The Geometry and Topology of Three-Manifolds by William P. Thurston Pdf

William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I–III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff. Volume IV contains Thurston's highly influential, though previously unpublished, 1977–78 Princeton Course Notes on the Geometry and Topology of 3-manifolds. It is an indispensable part of the Thurston collection but can also be used on its own as a textbook or for self-study.

Author : Danny Calegari
Publisher : Clarendon Press
Page : 384 pages
File Size : 51,8 Mb
Release : 2007-05-17
Category : Mathematics
ISBN : 9780191524639

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Foliations and the Geometry of 3-Manifolds by Danny Calegari Pdf

This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in 1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.

Author : William P. Thurston
Publisher : Princeton Mathematical Series
Page : 311 pages
File Size : 40,5 Mb
Release : 1997
Category : Geometry, Hyperbolic
ISBN : 0691083045

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Three-dimensional Geometry and Topology by William P. Thurston Pdf

Every mathematician should be acquainted with the basic facts about the geometry of surfaces, of two-dimensional manifolds. The theory of three-dimensional manifolds is much more difficult and still only partly understood, although there is ample evidence that the theory of three-dimensional manifolds is one of the most beautiful in the whole of mathematics. This excellent introductory work makes this mathematical wonderland remained rather inaccessible to non-specialists. The author is both a leading researcher, with a formidable geometric intuition, and a gifted expositor. His vivid descriptions of what it might be like to live in this or that three-dimensional manifold bring the subject to life. Like Poincaré, he appeals to intuition, but his enthusiasm is infectious and should make many converts for this kind of mathematics. There are good pictures, plenty of exercises and problems, and the reader will find a selection of topics which are not found in the standard repertoire. This book contains a great deal of interesting mathematics.

Author : Michael H. Freedman,Feng Luo
Publisher : American Mathematical Soc.
Page : 79 pages
File Size : 52,6 Mb
Release : 1989
Category : Mathematics
ISBN : 9780821870006

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Selected Applications of Geometry to Low-dimensional Topology by Michael H. Freedman,Feng Luo Pdf

The inaugural volume in the popular AMS softcover series designed to make more widely available some of the outstanding lectures presented by various faculty in North America.

Author : William P. Thurston
Publisher : Unknown
Page : 318 pages
File Size : 50,9 Mb
Release : 1991
Category : Geometry, Hyperbolic
ISBN : OCLC:33336219

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Three-dimensional geometry & topology by William P. Thurston Pdf

Author : A. T. Fomenko,A. A. Tuzhilin
Publisher : American Mathematical Soc.
Page : 156 pages
File Size : 40,9 Mb
Release : 2005
Category : Minimal surfaces
ISBN : 9780821837917

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Elements of the geometry and topology of minimal surfaces in three-dimensional space by A. T. Fomenko,A. A. Tuzhilin Pdf

This book grew out of lectures presented to students of mathematics, physics, and mechanics by A. T. Fomenko at Moscow University, under the auspices of the Moscow Mathematical Society. The book describes modern and visual aspects of the theory of minimal, two-dimensional surfaces in three-dimensional space. The main topics covered are: topological properties of minimal surfaces, stable and unstable minimal films, classical examples, the Morse-Smale index of minimal two-surfaces in Euclidean space, and minimal films in Lobachevskian space. Requiring only a standard first-year calculus and elementary notions of geometry, this book brings the reader rapidly into this fascinating branch of modern geometry.

Author : Glen E. Bredon
Publisher : Springer Science & Business Media
Page : 571 pages
File Size : 40,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475768480

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Topology and Geometry by Glen E. Bredon Pdf

This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS

Author : Hans U. Boden
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 48,5 Mb
Release : 2005
Category : Manifolds (Mathematics)
ISBN : 9780821837245

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Geometry and Topology of Manifolds by Hans U. Boden Pdf

This book contains expository papers that give an up-to-date account of recent developments and open problems in the geometry and topology of manifolds, along with several research articles that present new results appearing in published form for the first time. The unifying theme is the problem of understanding manifolds in low dimensions, notably in dimensions three and four, and the techniques include algebraic topology, surgery theory, Donaldson and Seiberg-Witten gauge theory,Heegaard Floer homology, contact and symplectic geometry, and Gromov-Witten invariants. The articles collected for this volume were contributed by participants of the Conference "Geometry and Topology of Manifolds" held at McMaster University on May 14-18, 2004 and are representative of the manyexcellent talks delivered at the conference.

Author : Vassily Olegovich Manturov,Louis H Kauffman
Publisher : World Scientific
Page : 540 pages
File Size : 41,7 Mb
Release : 2015-01-27
Category : Mathematics
ISBN : 9789814630634

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New Ideas In Low Dimensional Topology by Vassily Olegovich Manturov,Louis H Kauffman Pdf

This book consists of a selection of articles devoted to new ideas and developments 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.

Author : Werner Ballmann
Publisher : Birkhäuser
Page : 169 pages
File Size : 50,8 Mb
Release : 2018-07-18
Category : Mathematics
ISBN : 9783034809832

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Introduction to Geometry and Topology by Werner Ballmann Pdf

This book provides an introduction to topology, differential topology, and differential geometry. It is based on manuscripts refined through use in a variety of lecture courses. The first chapter covers elementary results and concepts from point-set topology. An exception is the Jordan Curve Theorem, which is proved for polygonal paths and is intended to give students a first glimpse into the nature of deeper topological problems. The second chapter of the book introduces manifolds and Lie groups, and examines a wide assortment of examples. Further discussion explores tangent bundles, vector bundles, differentials, vector fields, and Lie brackets of vector fields. This discussion is deepened and expanded in the third chapter, which introduces the de Rham cohomology and the oriented integral and gives proofs of the Brouwer Fixed-Point Theorem, the Jordan-Brouwer Separation Theorem, and Stokes's integral formula. The fourth and final chapter is devoted to the fundamentals of differential geometry and traces the development of ideas from curves to submanifolds of Euclidean spaces. Along the way, the book discusses connections and curvature--the central concepts of differential geometry. The discussion culminates with the Gauß equations and the version of Gauß's theorema egregium for submanifolds of arbitrary dimension and codimension. This book is primarily aimed at advanced undergraduates in mathematics and physics and is intended as the template for a one- or two-semester bachelor's course.

Author : Donal O'Shea
Publisher : Penguin UK
Page : 284 pages
File Size : 44,5 Mb
Release : 2008-10-30
Category : Science
ISBN : 9780141900346

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The Poincaré Conjecture by Donal O'Shea Pdf

The Poincaré Conjecture tells the story behind one of the world’s most confounding mathematical theories. Formulated in 1904 by Henri Poincaré, his Conjecture promised to describe the very shape of the universe, but remained unproved until a huge prize was offered for its solution in 2000. Six years later, an eccentric Russian mathematician had the answer. Here, Donal O’Shea explains the maths behind the Conjecture and its proof, and illuminates the curious personalities surrounding this perplexing conundrum, along the way taking in a grand sweep of scientific history from the ancient Greeks to Christopher Columbus. This is an enthralling tale of human endeavour, intellectual brilliance and the thrill of discovery.