Topology And Combinatorics Of 3 Manifolds

Author : Klaus Johannson
Publisher : Springer
ISBN 13 : 3540491813
Total Pages : 464 pages
Book Rating : 4.11/5 ( download)

DOWNLOAD NOW!

Download or read book Topology and Combinatorics of 3-Manifolds written by Klaus Johannson and published by Springer. This book was released on 2006-11-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Rubén Vigara
Publisher : World Scientific
ISBN 13 : 9814725501
Total Pages : 300 pages
Book Rating : 4.07/5 ( download)

DOWNLOAD NOW!

Download or read book Representing 3-Manifolds by Filling Dehn Surfaces written by Rubén Vigara and published by World Scientific. This book was released on 2016-03-11 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the beautiful and deep subject of filling Dehn surfaces in the study of topological 3-manifolds. This book presents, for the first time in English and with all the details, the results from the PhD thesis of the first author, together with some more recent results in the subject. It also presents some key ideas on how these techniques could be used on other subjects. Representing 3-Manifolds by Filling Dehn Surfaces is mostly self-contained requiring only basic knowledge on topology and homotopy theory. The complete and detailed proofs are illustrated with a set of more than 600 spectacular pictures, in the tradition of low-dimensional topology books. It is a basic reference for researchers in the area, but it can also be used as an advanced textbook for graduate students or even for adventurous undergraduates in mathematics. The book uses topological and combinatorial tools developed throughout the twentieth century making the volume a trip along the history of low-dimensional topology. Contents:Preliminaries:SetsManifoldsCurvesTransversalityRegular deformationsComplexesFilling Dehn Surfaces:Dehn Surfaces in 3-manifoldsFilling Dehn SurfacesNotationSurgery on Dehn Surfaces. Montesinos TheoremJohansson Diagrams:Diagrams Associated to Dehn SurfacesAbstract Diagrams on SurfacesThe Johansson TheoremFilling DiagramsFundamental Group of a Dehn Sphere:Coverings of Dehn SpheresThe Diagram GroupCoverings and RepresentationsApplicationsThe Fundamental Group of a Dehn g-torusFilling Homotopies:Filling HomotopiesBad Haken Moves"Not so Bad" Haken MovesDiagram MovesDuplicationAmendola's MovesProof of Theorem 5.8:Pushing DisksShellings. Smooth TriangulationsComplex f-movesInflating TriangulationsFilling PairsSimultaneous GrowingsProof of Theorem 5.8The Triple Point Spectrum:The Shima's SpheresSome Examples of Filling Dehn SurfacesThe Number of Triple Points as a Measure of Complexity: Montestinos ComplexityThe Triple Point SpectrumSurface-complexityKnots, Knots and Some Open Questions:2-Knots: Lifting Filling Dehn Surfaces1-KnotsOpen Problems Readership: Graduate students and researchers interested in low-dimensional topology. Key Features:It provides deep results in a new subject of mathematical research. Moreover, it introduces new mathematical tools and techniques useful in different areas of low-dimensional topologyThe book uses topological and combinatorial tools developed all along the twentieth century making the volume a trip along the history of low-dimensional topologyA spectacular set of pictures, in the better tradition of low-dimensional topology books, which give deep insight of the techniques and constructions done in the book

Author : Viktor Vasilʹevich Prasolov
Publisher : American Mathematical Soc.
ISBN 13 : 0821808982
Total Pages : 250 pages
Book Rating : 4.86/5 ( download)

DOWNLOAD NOW!

Download or read book Knots, Links, Braids and 3-Manifolds written by Viktor Vasilʹevich Prasolov and published by American Mathematical Soc.. This book was released on 1997 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the remarkable work of Vaughan Jones and Victor Vassiliev on knot and link invariants and its recent modifications and generalizations, including a mathematical treatment of Jones-Witten invariants. The mathematical prerequisites are minimal compared to other monographs in this area. Numerous figures and problems make this book suitable as a graduate level course text or for self-study.

Author : John Stillwell
Publisher : Springer Science & Business Media
ISBN 13 : 1461243726
Total Pages : 344 pages
Book Rating : 4.24/5 ( download)

DOWNLOAD NOW!

Download or read book Classical Topology and Combinatorial Group Theory written by John Stillwell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l'isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec tions to other parts of mathematics which make topology an important as well as a beautiful subject.

Author : John Hempel
Publisher : American Mathematical Soc.
ISBN 13 : 0821836951
Total Pages : 210 pages
Book Rating : 4.58/5 ( download)

DOWNLOAD NOW!

Download or read book 3-Manifolds written by John Hempel and published by American Mathematical Soc.. This book was released on 2004-11-02 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Michael Henle
Publisher : Courier Corporation
ISBN 13 : 9780486679662
Total Pages : 340 pages
Book Rating : 4.67/5 ( download)

DOWNLOAD NOW!

Download or read book A Combinatorial Introduction to Topology written by Michael Henle and published by Courier Corporation. This book was released on 1994-01-01 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.

Author : Jennifer Schultens
Publisher : American Mathematical Soc.
ISBN 13 : 1470410206
Total Pages : 298 pages
Book Rating : 4.09/5 ( download)

DOWNLOAD NOW!

Download or read book Introduction to 3-Manifolds written by Jennifer Schultens and published by American Mathematical Soc.. This book was released on 2014-05-21 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Danny Calegari
Publisher : Oxford University Press on Demand
ISBN 13 : 0198570082
Total Pages : 378 pages
Book Rating : 4.80/5 ( download)

DOWNLOAD NOW!

Download or read book Foliations and the Geometry of 3-Manifolds written by Danny Calegari and published by Oxford University Press on Demand. This book was released on 2007-05-17 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Rubén Vigara
Publisher :
ISBN 13 : 9789814725491
Total Pages : 276 pages
Book Rating : 4.98/5 ( download)

DOWNLOAD NOW!

Download or read book Representing 3-Manifolds by Filling Dehn Surfaces written by Rubén Vigara and published by . This book was released on 2016 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Viktor Vasilʹevich Prasolov
Publisher : American Mathematical Soc.
ISBN 13 : 0821838121
Total Pages : 432 pages
Book Rating : 4.29/5 ( download)

DOWNLOAD NOW!

Download or read book Elements of Homology Theory written by Viktor Vasilʹevich Prasolov and published by American Mathematical Soc.. This book was released on 2007 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a continuation of the previous book by the author (Elements of Combinatorial and Differential Topology, Graduate Studies in Mathematics, Volume 74, American Mathematical Society, 2006). It starts with the definition of simplicial homology and cohomology, with many examples and applications. Then the Kolmogorov-Alexander multiplication in cohomology is introduced. A significant part of the book is devoted to applications of simplicial homology and cohomology to obstruction theory, in particular, to characteristic classes of vector bundles. The later chapters are concerned with singular homology and cohomology, and Cech and de Rham cohomology. The book ends with various applications of homology to the topology of manifolds, some of which might be of interest to experts in the area. The book contains many problems; almost all of them are provided with hints or complete solutions.