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The Poincare Conjecture: In Search of the Shape of the Universe
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Donal O'Shea
In telling this vibrant story, O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians.
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The Shape of Space: How to Visualize Surfaces and Three-Dimensional Manifolds
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Jeffrey Weeks
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An Extension of Casson's Invariant
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Kevin Walker
This book describes an invariant, l, of oriented rational homology 3-spheres which is a generalization of work of Andrew Casson in the integer homology sphere case. Let R(X) denote the space of conjugacy classes of representations of p(X) into SU(2). Let (W,W,F) be a Heegaard splitting of a rational homology sphere M. Then l(M) is declared to be ...
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Algorithmic Topology and Classification of 3-Manifolds
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Sergei Matveev
The below mentioned are from the reviews of the 1st edition: 'This book provides a comprehensive and detailed account of different topics in algorithmic 3-dimensional topology, culminating with the recognition procedure for Haken manifolds and including the up-to-date results in computer enumeration of 3-manifolds. Originating from lecture notes ...
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Spaces of Kleinian Groups
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Yair Minsky (Editor), Makoto Sakuma (Editor), Caroline Series (Editor)
The subject of Kleinian groups and hyperbolic 3-manifolds is currently undergoing explosively fast development, the last few years having seen the resolution of many longstanding conjectures. This volume contains important expositions and original work by some of the main contributors on topics such as topology and geometry of 3-manifolds, curve ...
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The Arithmetic of Hyperbolic 3-Manifolds
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Colin M MacLachlan, Alan W Reid
For the past 25 years, the Geometrization Program of Thurston has been a driving force for research in 3-manifold topology. This has inspired a surge of activity investigating hyperbolic 3-manifolds (and Kleinian groups), as these manifolds form the largest and least well- understood class of compact 3-manifolds. Familiar and new tools from ...
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Renormalization and 3-Manifolds Which Fiber Over the Circle (Am-142)
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Curtis T McMullen
Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. Both subjects are studied via geometric ...
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Spherical Cr Geometry and Dehn Surgery
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Richard Evan Schwartz
This book proves an analogue of William Thurston's celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it. The first is the construction of large numbers of closed real hyperbolic 3-manifolds which bound complex hyperbolic orbifolds - the only known ...
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Kleinian Groups and Hyperbolic 3-Manifolds: Proceedings of the Warwick Workshop, September 11-14, 2001
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Yohei Komori (Editor), Vladimir Markovic (Editor), Caroline Series (Editor)
The subject of Kleinian groups and hyperbolic 3-manifolds is currently undergoing explosively fast development, with many old problems and conjectures close to resolution. This volume, proceedings of the Warwick workshop in September 2001, contains expositions of many of these breakthroughs including Minsky's lectures on the first half of the ...
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Invariants of Homology 3-Spheres
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R V Gamkrelidze (Editor), Nikolai Saveliev, A Vassiiev (Editor)
Homology 3-sphere is a closed 3-dimensional manifold whose homology equals that of the 3-sphere. These objects may look rather special but they have played an outstanding role in geometric topology for the past fifty years. The book gives a systematic exposition of diverse ideas and methods in the area, from algebraic topology of manifolds to ...
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Global Surgery Formula for the Casson-Walker Invariant. (Am-140)
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Christine Lescop
This book presents a new result in 3-dimensional topology. It is well known that any closed oriented 3-manifold can be obtained by surgery on a framed link in S3. In "Global Surgery Formula for the Casson-Walker Invariant", a function F of framed links in S3 is described, and it is proven that F consistently defines an invariant, lamda (l), of ...
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Chern-Simons Theory, Matrix Models, and Topological Strings
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by
Marcos Marino
In recent years, the old idea that gauge theories and string theories are equivalent has been implemented and developed in various ways, and there are by now various models where the string theory / gauge theory correspondence is at work. One of the most important examples of this correspondence relates Chern-Simons theory, a topological gauge ...
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Casson's Invariant for Oriented Homology 3-Spheres: An Exposition
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Selman Akbulut, Selman Akbulat, John D McCarthy
In the spring of 1985, A. Casson announced an interesting invariant of homology 3-spheres via constructions on representation spaces. This invariant generalizes the Rohlin invariant and gives surprising corollaries in low-dimensional topology. In the fall of that same year, Selman Akbulut and John McCarthy held a seminar on this invariant. These ...
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3-manifolds
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by
John Hempel
For many years, John Hempel's book has been a standard text on the topology of 3-manifolds. Even though the field has grown tremendously, the book remains one of the best and most popular introductions to the subject. The theme of this book is the role of the fundamental group in determining the topology of a given 3-manifold. The essential ideas ...
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Monopoles and Three-Manifolds
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Peter Kronheimer, Tomasz Mrowka
Originating with Andreas Floer in the 1980s, Floer homology has proved to be an effective tool in tackling many important problems in three- and four-dimensional geometry, and topology. This book provides a comprehensive treatment of Floer homology, based on the Seiberg-Witten monopole equations. After first providing an overview of the results, ...
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Outer Circles: An Introduction to Hyperbolic 3-Manifolds
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by
A Marden
We live in a three-dimensional space; what sort of space is it? Can we build it from simple geometric objects? The answers to such questions have been found in the last 30 years, and Outer Circles describes the basic mathematics needed as well as making clear the grand design of the subject of hyperbolic manifolds as a whole. This picture is ...
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Elliptic structures on 3-manifolds
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by
Thomas
This volume will give a systematic exposition of known results for free actions by finite groups on S. The text begins with preliminary material on Seifert manifolds and group classification. This is followed by sections dealing with related topics including free bZe/2 and bZe/3 actions on lens/prism manifolds, the reduction theorem and tangential ...
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Surgery on Contact 3-Manifolds and Stein Surfaces
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Burak Ozbagci, Andras I Stipsicz, Andrs I Stipsicz
This book is about an investigation of recent developments in the field of symplectic and contact structures on four and three dimensional manifolds, respectively, from a topologist's point of view. The level of the book is appropriate for advanced graduate students. There is no doubt that symplectic and contact structures are in the center of ...
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Lecture Notes on Chern-Simons-Witten the
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Sen Hu
This monograph has arisen in part from E. Witten's lectures on topological quantum field theory given in the spring of 1989 at Princeton University. At that time, Witten unified several important mathematical works in terms of quantum field theory, most notably the Donaldson polynomial, the Gromov-Floer homology and the Jones polynomials. In this ...
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Lectures on Three-Manifold Topology
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by
William H. Jaco, Conference Board of the Mathematical Sci
This manuscript is a detailed presentation of the ten lectures given by the author at the NSF Regional Conference on Three-Manifold Topology, held October 1977, at Virginia Polytechnic Institute and State University. The purpose of the conference was to present the current state of affairs in three-manifold topology and to integrate the classical ...
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Knots, Groups, and 3-Manifolds: Papers Dedicated to the Memory of R. H. Fox
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L. P. Neuwirth
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Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds
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Louis H Kauffman, Louis H Kaufmann, Sosteness Lins
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 ...
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Algorithmic and Computer Methods for Three-Manifolds
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by
A T Fomenko, S V Matveev
This monograph presents a comprehensive coverage of three-dimensional topology, as well as exploring some of its frontiers. Many important applied problems of mechanics and theoretical physics can be reduced to algorithmic problems of three-dimensional topology, which can then be solved using computers. Although much progress in this field has ...
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Link Theory in Manifolds
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by
Uwe Kaiser
Any topological theory of knots and links should be based on simple ideas of intersection and linking. In this book, a general theory of link bordism in manifolds and universal constructions of linking numbers in oriented 3-manifolds are developed. In this way, classical concepts of link theory in the 3-spheres are generalized to a certain class ...
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Branched Standard Spines of 3-Manifolds
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Riccardo Benedetti, Carlo Petronio
This text provides a unified combinatorial realization of the categories of (closed, oriented) 3-manifolds, combed 3-manifolds, framed 3-manifolds and spin 3-manifolds. In all four cases the objects of the realization are finite enhanced graphs. These realizations are based on the notion of branched standard spine, introduced in the book as a ...
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