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Author : Darryl McCullough
Publisher :
ISBN 13 :
Total Pages : 104 pages
Book Rating : 4.3/5 (91 download)
Download or read book 3-manifolds and Their Mappings written by Darryl McCullough and published by . This book was released on 1995 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John Hempel
Publisher : American Mathematical Soc.
ISBN 13 : 0821836951
Total Pages : 210 pages
Book Rating : 4.8/5 (218 download)
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 : Danny Calegari
Publisher : Oxford University Press on Demand
ISBN 13 : 0198570082
Total Pages : 378 pages
Book Rating : 4.1/5 (985 download)
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 : Tomotada Ohtsuki
Publisher : World Scientific
ISBN 13 : 9814490717
Total Pages : 508 pages
Book Rating : 4.8/5 (144 download)
Download or read book Quantum Invariants: A Study Of Knots, 3-manifolds, And Their Sets written by Tomotada Ohtsuki and published by World Scientific. This book was released on 2001-12-21 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The Chern-Simons field theory and the Wess-Zumino-Witten model are described as the physical background of the invariants.
Author : Peter W. Michor
Publisher :
ISBN 13 :
Total Pages : 176 pages
Book Rating : 4.3/5 (91 download)
Download or read book Manifolds of Differentiable Mappings written by Peter W. Michor and published by . This book was released on 1980 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : William H. Jaco
Publisher : American Mathematical Soc.
ISBN 13 : 0821822209
Total Pages : 204 pages
Book Rating : 4.8/5 (218 download)
Download or read book Seifert Fibered Spaces in 3-Manifolds written by William H. Jaco and published by American Mathematical Soc.. This book was released on 1979 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theorem of this monograph, or rather the "absolute" case of the main theorem, provides what is essentially a homotopy-classification of suitably "nondegenerate" maps of Seifert-fibered 3-manifolds into a sufficiently-large, compact, irreducible, orientable 3-manifold M.
Author : Alden Halbert Wright
Publisher :
ISBN 13 :
Total Pages : 190 pages
Book Rating : 4.:/5 (89 download)
Download or read book Monotone Mappings of Compact 3-manifolds written by Alden Halbert Wright and published by . This book was released on 1969 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jennifer Schultens
Publisher : American Mathematical Soc.
ISBN 13 : 1470410206
Total Pages : 298 pages
Book Rating : 4.4/5 (74 download)
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 : Mathematical Sciences Research Institute (Berkeley, Calif.).
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (218 download)
Download or read book Mappings of Reducible 3-manifolds written by Mathematical Sciences Research Institute (Berkeley, Calif.). and published by . This book was released on 1984 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Franc Forstnerič
Publisher : Springer
ISBN 13 : 3319610589
Total Pages : 569 pages
Book Rating : 4.3/5 (196 download)
Download or read book Stein Manifolds and Holomorphic Mappings written by Franc Forstnerič and published by Springer. This book was released on 2017-09-05 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, now in a carefully revised second edition, provides an up-to-date account of Oka theory, including the classical Oka-Grauert theory and the wide array of applications to the geometry of Stein manifolds. Oka theory is the field of complex analysis dealing with global problems on Stein manifolds which admit analytic solutions in the absence of topological obstructions. The exposition in the present volume focuses on the notion of an Oka manifold introduced by the author in 2009. It explores connections with elliptic complex geometry initiated by Gromov in 1989, with the Andersén-Lempert theory of holomorphic automorphisms of complex Euclidean spaces and of Stein manifolds with the density property, and with topological methods such as homotopy theory and the Seiberg-Witten theory. Researchers and graduate students interested in the homotopy principle in complex analysis will find this book particularly useful. It is currently the only work that offers a comprehensive introduction to both the Oka theory and the theory of holomorphic automorphisms of complex Euclidean spaces and of other complex manifolds with large automorphism groups.
Author : R. H. Bing
Publisher :
ISBN 13 :
Total Pages : 38 pages
Book Rating : 4.3/5 (91 download)
Download or read book Topology of 3-manifolds written by R. H. Bing and published by . This book was released on 1970 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a summary of four Colloquium Lectures given at the meeting of the American Mathematical Society in Laramie in 1970. The first section discusses the recent solution of the monotone mapping theorem. The second discusses difficulty and headway in extending results about 3-manifolds to those of higher dimensions. The last two sections discuss approximation theorems and their applications. (Author).
Author : K. Johannson
Publisher : Springer
ISBN 13 : 3540384863
Total Pages : 312 pages
Book Rating : 4.5/5 (43 download)
Download or read book Homotopy Equivalences of 3-Manifolds with Boundaries written by K. Johannson and published by Springer. This book was released on 2006-11-15 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard Douglas Canary
Publisher : American Mathematical Soc.
ISBN 13 : 0821835491
Total Pages : 238 pages
Book Rating : 4.8/5 (218 download)
Download or read book Homotopy Equivalences of 3-Manifolds and Deformation Theory of Kleinian Groups written by Richard Douglas Canary and published by American Mathematical Soc.. This book was released on 2004 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Three volume narrative history of 20th century.
Author : Mary-Elizabeth Hamstrom
Publisher : American Mathematical Soc.
ISBN 13 : 0821812408
Total Pages : 47 pages
Book Rating : 4.8/5 (218 download)
Download or read book Regular Mappings and the Space of Homeomorphisms on a 3-Manifold written by Mary-Elizabeth Hamstrom and published by American Mathematical Soc.. This book was released on 1961 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Darryl McCullough
Publisher : American Mathematical Soc.
ISBN 13 : 0821823469
Total Pages : 117 pages
Book Rating : 4.8/5 (218 download)
Download or read book Homeomorphisms of $3$-Manifolds with Compressible Boundary written by Darryl McCullough and published by American Mathematical Soc.. This book was released on 1986 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the mapping class groups of orientable [italic]P2-irreducible 3-manifolds with compressible boundary, and extend the results proved by K. Johannson for the boundary incompressible case. The authors show that the mapping class group is finitely-generated and has a geometrically defined subgroup of finite index. The main tool used in the proof of the results is to reduce the theorems to analogous statements about incompressible neighborhoods of compressible boundary components, and, using the fact that they have a very simple structure (being products-with-handles), to apply geometric techniques. Appropriate extensions of the results of the nonorientable [italic]P2-irreducible 3-manifolds are also given.
Author : Sergei Matveev
Publisher : Springer Science & Business Media
ISBN 13 : 3662051028
Total Pages : 487 pages
Book Rating : 4.6/5 (62 download)
Download or read book Algorithmic Topology and Classification of 3-Manifolds written by Sergei Matveev and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Vladimir G. Turaev
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110435225
Total Pages : 608 pages
Book Rating : 4.1/5 (14 download)
Download or read book Quantum Invariants of Knots and 3-Manifolds written by Vladimir G. Turaev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-07-11 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to the strong appeal and wide use of this monograph, it is now available in its third revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups. The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space. This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. Contents: Invariants of graphs in Euclidean 3-space and of closed 3-manifolds Foundations of topological quantum field theory Three-dimensional topological quantum field theory Two-dimensional modular functors 6j-symbols Simplicial state sums on 3-manifolds Shadows of manifolds and state sums on shadows Constructions of modular categories
