3 Manifolds

Author : Jennifer Schultens
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 48,7 Mb
Release : 2014-05-21
Category : Mathematics
ISBN : 9781470410209

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Introduction to 3-Manifolds by Jennifer Schultens Pdf

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.

Author : Sergei Matveev
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 46,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662051023

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Algorithmic Topology and Classification of 3-Manifolds by Sergei Matveev Pdf

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 : Danny Calegari
Publisher : Oxford University Press on Demand
Page : 378 pages
File Size : 47,9 Mb
Release : 2007-05-17
Category : Mathematics
ISBN : 9780198570080

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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 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 : Anonim
Publisher : European Mathematical Society
Page : 256 pages
File Size : 44,5 Mb
Release : 2010
Category : Covering spaces (Topology)
ISBN : 3037190825

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Geometrisation of 3-manifolds by Anonim Pdf

The Geometrisation Conjecture was proposed by William Thurston in the mid 1970s in order to classify compact 3-manifolds by means of a canonical decomposition along essential, embedded surfaces into pieces that possess geometric structures. It contains the famous Poincaré Conjecture as a special case. In 2002, Grigory Perelman announced a proof of the Geometrisation Conjecture based on Richard Hamilton’s Ricci flow approach, and presented it in a series of three celebrated arXiv preprints. Since then there has been an ongoing effort to understand Perelman’s work by giving more detailed and accessible presentations of his ideas or alternative arguments for various parts of the proof. This book is a contribution to this endeavour. Its two main innovations are first a simplified version of Perelman’s Ricci flow with surgery, which is called Ricci flow with bubbling-off, and secondly a completely different and original approach to the last step of the proof. In addition, special effort has been made to simplify and streamline the overall structure of the argument, and make the various parts independent of one another. A complete proof of the Geometrisation Conjecture is given, modulo pre-Perelman results on Ricci flow, Perelman’s results on the ℒ-functional and κ-solutions, as well as the Colding–Minicozzi extinction paper. The book can be read by anyone already familiar with these results, or willing to accept them as black boxes. The structure of the proof is presented in a lengthy introduction, which does not require knowledge of geometric analysis. The bulk of the proof is the existence theorem for Ricci flow with bubbling-off, which is treated in parts I and II. Part III deals with the long time behaviour of Ricci flow with bubbling-off. Part IV finishes the proof of the Geometrisation Conjecture.

Author : K. Johannson
Publisher : Springer
Page : 312 pages
File Size : 43,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540384861

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Homotopy Equivalences of 3-Manifolds with Boundaries by K. Johannson Pdf

Author : Colin Maclachlan,Alan W. Reid
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 44,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475767209

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The Arithmetic of Hyperbolic 3-Manifolds by Colin Maclachlan,Alan W. Reid Pdf

Recently there has been considerable interest in developing techniques based on number theory to attack problems of 3-manifolds; Contains many examples and lots of problems; Brings together much of the existing literature of Kleinian groups in a clear and concise way; At present no such text exists

Author : Klaus Johannson
Publisher : Springer
Page : 464 pages
File Size : 51,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540491811

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Topology and Combinatorics of 3-Manifolds by Klaus Johannson Pdf

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

Author : Nikolai Saveliev
Publisher : Walter de Gruyter
Page : 212 pages
File Size : 51,9 Mb
Release : 2012-10-25
Category : Mathematics
ISBN : 9783110806359

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Lectures on the Topology of 3-Manifolds by Nikolai Saveliev Pdf

Author : Burak Ozbagci,András Stipsicz
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 52,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662101674

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Surgery on Contact 3-Manifolds and Stein Surfaces by Burak Ozbagci,András Stipsicz Pdf

This book is about an investigation of recent developments in the field of sympletic and contact structures on four- and three-dimensional manifolds from a topologist’s point of view. In it, two main issues are addressed: what kind of sympletic and contact structures we can construct via surgery theory and what kind of sympletic and contact structures are not allowed via gauge theory and the newly invented Heegaard-Floer theory.

Author : Ralph Hartzler Fox,Lee Paul Neuwirth
Publisher : Princeton University Press
Page : 356 pages
File Size : 55,7 Mb
Release : 1975-08-21
Category : Mathematics
ISBN : 0691081700

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Knots, Groups, and 3-manifolds by Ralph Hartzler Fox,Lee Paul Neuwirth Pdf

There is a sympathy of ideas among the fields of knot theory, infinite discrete group theory, and the topology of 3-manifolds. This book contains fifteen papers in which new results are proved in all three of these fields. These papers are dedicated to the memory of Ralph H. Fox, one of the world's leading topologists, by colleagues, former students, and friends. In knot theory, papers have been contributed by Goldsmith, Levine, Lomonaco, Perko, Trotter, and Whitten. Of these several are devoted to the study of branched covering spaces over knots and links, while others utilize the braid groups of Artin. Cossey and Smythe, Stallings, and Strasser address themselves to group theory. In his contribution Stallings describes the calculation of the groups In/In+1 where I is the augmentation ideal in a group ring RG. As a consequence, one has for each k an example of a k-generator l-relator group with no free homomorphs. In the third part, papers by Birman, Cappell, Milnor, Montesinos, Papakyriakopoulos, and Shalen comprise the treatment of 3-manifolds. Milnor gives, besides important new results, an exposition of certain aspects of our current knowledge regarding the 3- dimensional Brieskorn manifolds.

Author : Vladimir Turaev
Publisher : Birkhäuser
Page : 201 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034879996

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Torsions of 3-dimensional Manifolds by Vladimir Turaev Pdf

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

Author : Jean-Pierre Otal
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 46,5 Mb
Release : 2001
Category : Mathematics
ISBN : 0821821539

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The Hyperbolization Theorem for Fibered 3-Manifolds by Jean-Pierre Otal Pdf

For graduate students familiar with low-dimensional topology and researchers in geometry and topology, Otal (CNRS-UMR 128, Lyon) offers a complete proof of Thurston's hyperbolization theorem for 3-manifolds that fiber as surface bundles. The original Le Theoreme d'Hyperbolisation pour les Varietes de Dimension 3, published by the French Mathematical Society in 1996, has been translated by Leslie D. Kay. c. Book News Inc.

Author : John Hempel
Publisher : American Mathematical Society
Page : 209 pages
File Size : 54,5 Mb
Release : 2022-09-21
Category : Mathematics
ISBN : 9781470471644

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3-Manifolds by John Hempel Pdf

A careful and systematic development of the theory of the topology of 3-manifolds, focusing on the critical role of the fundamental group in determining the topological structure of a 3-manifold … self-contained … one can learn the subject from it … would be very appropriate as a text for an advanced graduate course or as a basis for a working seminar. —Mathematical Reviews 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 and techniques are covered in the first part of the book: Heegaard splittings, connected sums, the loop and sphere theorems, incompressible surfaces, free groups, and so on. Along the way, many useful and insightful results are proved, usually in full detail. Later chapters address more advanced topics, including Waldhausen's theorem on a class of 3-manifolds that is completely determined by its fundamental group. The book concludes with a list of problems that were unsolved at the time of publication. Hempel's book remains an ideal text to learn about the world of 3-manifolds. The prerequisites are few and are typical of a beginning graduate student. Exercises occur throughout the text.

Author : A.T. Fomenko,S.V. Matveev
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 40,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401706995

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Algorithmic and Computer Methods for Three-Manifolds by A.T. Fomenko,S.V. Matveev Pdf

One service mathematics has rendered the human race. It has put common sense back where it belongs. It has put common sense back where it belongs, on the topmost shelf next to the dusty canister labelled discarded nonsense. Eric TBell Every picture tells a story. Advenisement for for Sloan's backache and kidney oils, 1907 The book you have in your hands as you are reading this, is a text on3-dimensional topology. It can serve as a pretty comprehensive text book on the subject. On the other hand, it frequently gets to the frontiers of current research in the topic. If pressed, I would initially classify it as a monograph, but, thanks to the over three hundred illustrations of the geometrical ideas involved, as a rather accessible one, and hence suitable for advanced classes. The style is somewhat informal; more or less like orally presented lectures, and the illustrations more than make up for all the visual aids and handwaving one has at one's command during an actual presentation.

Author : Viacheslav Z. Grines,Timur V. Medvedev,Olga V. Pochinka
Publisher : Springer
Page : 295 pages
File Size : 52,9 Mb
Release : 2016-11-11
Category : Mathematics
ISBN : 9783319448473

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Dynamical Systems on 2- and 3-Manifolds by Viacheslav Z. Grines,Timur V. Medvedev,Olga V. Pochinka Pdf

This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A. The main results on the topological classification of discrete dynamical systems are widely scattered among many papers and surveys. This book presents these results fluidly, systematically, and for the first time in one publication. Additionally, this book discusses the recent results on the topological classification of Axiom A diffeomorphisms focusing on the nontrivial effects of the dynamical systems on 2- and 3-manifolds. The classical methods and approaches which are considered to be promising for the further research are also discussed.“br> The reader needs to be familiar with the basic concepts of the qualitative theory of dynamical systems which are presented in Part 1 for convenience. The book is accessible to ambitious undergraduates, graduates, and researchers in dynamical systems and low dimensional topology. This volume consists of 10 chapters; each chapter contains its own set of references and a section on further reading. Proofs are presented with the exact statements of the results. In Chapter 10 the authors briefly state the necessary definitions and results from algebra, geometry and topology. When stating ancillary results at the beginning of each part, the authors refer to other sources which are readily available.