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Author: Matthew G. Brin
Publisher: American Mathematical Soc.
ISBN: 0821824740
Category : Homotopy theory
Languages : en
Pages : 86
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Book Description
This paper continues a series by the authors on non-compact 3-manifolds. We describe the structure, up to end homeomorphism, of those orientable, non-compact 3-manifolds in which all loops near infinity [symbol] homotop to infinity [symbol] while staying near infinity [symbol] (the proper homotopy condition "end 1-movability" of the title). This extends previous work by others and by the authors because end 1-movability is weaker than properties studied before, and also because our result is the first to analyse a class of non-compact 3-manifolds whose defining properties include neither irreducibilty nor compact boundary. Our main tool is the end reduction--introduced in our earlier papers, developed further. End reductions are "simple" approximations of a non-compact 3-manifold that capture many of the manifold's properties.
Author: Matthew G. Brin
Publisher: American Mathematical Soc.
ISBN: 0821824740
Category : Homotopy theory
Languages : en
Pages : 86
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Book Description
This paper continues a series by the authors on non-compact 3-manifolds. We describe the structure, up to end homeomorphism, of those orientable, non-compact 3-manifolds in which all loops near infinity [symbol] homotop to infinity [symbol] while staying near infinity [symbol] (the proper homotopy condition "end 1-movability" of the title). This extends previous work by others and by the authors because end 1-movability is weaker than properties studied before, and also because our result is the first to analyse a class of non-compact 3-manifolds whose defining properties include neither irreducibilty nor compact boundary. Our main tool is the end reduction--introduced in our earlier papers, developed further. End reductions are "simple" approximations of a non-compact 3-manifold that capture many of the manifold's properties.
Author: William P. Thurston
Publisher: American Mathematical Society
ISBN: 1470474743
Category : Mathematics
Languages : en
Pages : 337
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Book Description
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: Oxford University Press on Demand
ISBN: 0198570082
Category : Mathematics
Languages : en
Pages : 378
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Book Description
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 in1-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: Tomasz Mrowka
Publisher: American Mathematical Soc.
ISBN: 0821886967
Category : Mathematics
Languages : en
Pages : 331
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Book Description
Low-dimensional topology has long been a fertile area for the interaction of many different disciplines of mathematics, including differential geometry, hyperbolic geometry, combinatorics, representation theory, global analysis, classical mechanics, and theoretical physics. The Park City Mathematics Institute summer school in 2006 explored in depth the most exciting recent aspects of this interaction, aimed at a broad audience of both graduate students and researchers. The present volume is based on lectures presented at the summer school on low-dimensional topology. These notes give fresh, concise, and high-level introductions to these developments, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field of low-dimensional topology and to senior researchers wishing to keep up with current developments. The volume begins with notes based on a special lecture by John Milnor about the history of the topology of manifolds. It also contains notes from lectures by Cameron Gordon on the basics of three-manifold topology and surgery problems, Mikhail Khovanov on his homological invariants for knots, John Etnyre on contact geometry, Ron Fintushel and Ron Stern on constructions of exotic four-manifolds, David Gabai on the hyperbolic geometry and the ending lamination theorem, Zoltan Szabo on Heegaard Floer homology for knots and three manifolds, and John Morgan on Hamilton's and Perelman's work on Ricci flow and geometrization.
Author: Bruce Hughes
Publisher: Cambridge University Press
ISBN: 0521576253
Category : Mathematics
Languages : en
Pages : 384
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Book Description
A systematic exposition of the theory and practice of ends of manifolds and CW complexes, not previously available.
Author: Akio Kawauchi
Publisher: Birkhäuser
ISBN: 3034892276
Category : Mathematics
Languages : en
Pages : 431
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Book Description
Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory.
Author: Louis H. Kauffman
Publisher: Princeton University Press
ISBN: 1400882532
Category : Mathematics
Languages : en
Pages : 308
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Book Description
This book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of links are constructed and combined to form the 3-manifold invariants. The methods in this book are based on a recoupling theory for the Temperley-Lieb algebra. This recoupling theory is a q-deformation of the SU(2) spin networks of Roger Penrose. The recoupling theory is developed in a purely combinatorial and elementary manner. Calculations are based on a reformulation of the Kirillov-Reshetikhin shadow world, leading to expressions for all the invariants in terms of state summations on 2-cell complexes. Extensive tables of the invariants are included. Manifolds in these tables are recognized by surgery presentations and by means of 3-gems (graph encoded 3-manifolds) in an approach pioneered by Sostenes Lins. The appendices include information about gems, examples of distinct manifolds with the same invariants, and applications to the Turaev-Viro invariant and to the Crane-Yetter invariant of 4-manifolds.
Author: Sergei Matveev
Publisher: Springer Science & Business Media
ISBN: 3662051028
Category : Mathematics
Languages : en
Pages : 487
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Book Description
Here is a thorough review of topics in 3-dimensional topology, derived from a decade of courses taught by the author. The author keeps the exposition to an elementary level by presenting the material mainly from the point of view of special polyhedra and special spines of 3-manifolds. The book culminates with the recognition procedure for Haken manifolds, and includes up-to-date results in computer enumeration of 3-mainfolds. The second edition adds new results, new proofs, and commentaries. Algorithmic Topology and Classification of 3-Manifolds serves as a standard reference for algorithmic 3-dimensional topology for both graduate students and researchers.
Author: Sostenes Lins
Publisher: World Scientific
ISBN: 9814501530
Category : Mathematics
Languages : en
Pages : 468
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Book Description
This book is about dealing with 3-manifolds using computers. Its emphasis is on presenting algorithms which are used for solving (in practice) the homeomorphism problem for the smallest of these objects. The key concept is the 3-gem, a special kind of edge-colored graph, which encodes the manifold via a ball complex. Passages between 3-gems and more standard presentations like Heegaard diagrams and surgery descriptions are provided. A catalogue of all closed orientable 3-manifolds induced by 3-gems up to 30 vertices is included. In order to help the classification, various invariants are presented, including the new quantum invariants.
Author: Michel Boileau
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 180
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Book Description
Orbifolds locally look like quotients of manifolds by finite group actions. They play an important role in the study of proper actions of discrete groups on manifolds. This monograph presents recent fundamental results on the geometry and topology of 3-dimensional orbifolds, with an emphasis on their geometric properties. It is suitable for graduate students and research mathematicians interested in geometry and topology.
