Lectures on the Topology of 3-manifolds
| Author | : Nikolai Saveliev |
| Publisher | : Walter de Gruyter |
| Total Pages | : 220 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 9783110162721 |
Topology Of 3 Manifolds
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Introduction to 3-Manifolds
| Author | : Jennifer Schultens |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 298 |
| Release | : 2014-05-21 |
| Genre | : Mathematics |
| ISBN | : 1470410206 |
This book grew out of a graduate course on 3-manifolds and is intended for a mathematically experienced audience that is new to low-dimensional topology. The exposition begins with the definition of a manifold, explores possible additional structures on manifolds, discusses the classification of surfaces, introduces key foundational results for 3-manifolds, and provides an overview of knot theory. It then continues with more specialized topics by briefly considering triangulations of 3-manifolds, normal surface theory, and Heegaard splittings. The book finishes with a discussion of topics relevant to viewing 3-manifolds via the curve complex. With about 250 figures and more than 200 exercises, this book can serve as an excellent overview and starting point for the study of 3-manifolds.
Algorithmic Topology and Classification of 3-Manifolds
| Author | : Sergei Matveev |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 487 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 3662051028 |
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.
Topology and Combinatorics of 3-Manifolds
| Author | : Klaus Johannson |
| Publisher | : Springer |
| Total Pages | : 464 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540491813 |
This book is a study of combinatorial structures of 3-mani- folds, especially Haken 3-manifolds. Specifically, it is concerned with Heegard graphs in Haken 3-manifolds, i.e., with graphs whose complements have a free fundamental group. These graphs always exist. They fix not only a combinatorial stucture but also a presentation for the fundamental group of the underlying 3-manifold. The starting point of the book is the result that the intersection of Heegard graphs with incompressible surfaces, or hierarchies of such surfaces, is very rigid. A number of finiteness results lead up to a ri- gidity theorem for Heegard graphs. The book is intended for graduate students and researchers in low-dimensional topolo- gy as well as combinatorial theory. It is self-contained and requires only a basic knowledge of the theory of 3-manifolds
The Geometry and Topology of Three-Manifolds
| Author | : William P. Thurston |
| Publisher | : American Mathematical Society |
| Total Pages | : 337 |
| Release | : 2023-06-16 |
| Genre | : Mathematics |
| ISBN | : 1470474743 |
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.
The Geometric Topology of 3-manifolds
| Author | : R. H. Bing |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 250 |
| Release | : 1983-12-31 |
| Genre | : Mathematics |
| ISBN | : 0821810405 |
Suitable for students and researchers in topology. this work provides the reader with an understanding of the physical properties of Euclidean 3-space - the space in which we presume we live.
Torsions of 3-dimensional Manifolds
| Author | : Vladimir Turaev |
| Publisher | : Birkhäuser |
| Total Pages | : 201 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034879997 |
From the reviews: "This is an excellent exposition about abelian Reidemeister torsions for three-manifolds." —Zentralblatt Math "This monograph contains a wealth of information many topologists will find very handy. ...Many of the new points of view pioneered by Turaev are gradually becoming mainstream and are spreading beyond the pure topology world. This monograph is a timely and very useful addition to the scientific literature." —Mathematical Reviews
Three-dimensional Geometry and Topology
| Author | : William P. Thurston |
| Publisher | : Princeton University Press |
| Total Pages | : 340 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 9780691083049 |
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.
Lectures on Three-Manifold Topology
| Author | : William H. Jaco |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 266 |
| Release | : 1980-12-31 |
| Genre | : Mathematics |
| ISBN | : 0821816934 |
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 results with the many recent advances and new directions.
Foliations and the Geometry of 3-Manifolds
| Author | : Danny Calegari |
| Publisher | : Oxford University Press on Demand |
| Total Pages | : 378 |
| Release | : 2007-05-17 |
| Genre | : Mathematics |
| ISBN | : 0198570082 |
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.
