Knots, Groups and 3-Manifolds (AM-84), Volume 84

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Publisher : Princeton University Press
ISBN 13 : 140088151X
Total Pages : 352 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Knots, Groups and 3-Manifolds (AM-84), Volume 84 by : Lee Paul Neuwirth

Download or read book Knots, Groups and 3-Manifolds (AM-84), Volume 84 written by Lee Paul Neuwirth and published by Princeton University Press. This book was released on 2016-03-02 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

In the Tradition of Thurston

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Publisher : Springer Nature
ISBN 13 : 3030559289
Total Pages : 724 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis In the Tradition of Thurston by : Ken’ichi Ohshika

Download or read book In the Tradition of Thurston written by Ken’ichi Ohshika and published by Springer Nature. This book was released on 2020-12-07 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of 16 surveys on Thurston's work and its later development. The authors are mathematicians who were strongly influenced by Thurston's publications and ideas. The subjects discussed include, among others, knot theory, the topology of 3-manifolds, circle packings, complex projective structures, hyperbolic geometry, Kleinian groups, foliations, mapping class groups, Teichmüller theory, anti-de Sitter geometry, and co-Minkowski geometry. The book is addressed to researchers and students who want to learn about Thurston’s wide-ranging mathematical ideas and their impact. At the same time, it is a tribute to Thurston, one of the greatest geometers of all time, whose work extended over many fields in mathematics and who had a unique way of perceiving forms and patterns, and of communicating and writing mathematics.

The Branched Cyclic Coverings of 2 Bridge Knots and Links

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Publisher : American Mathematical Soc.
ISBN 13 : 0821822551
Total Pages : 75 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Branched Cyclic Coverings of 2 Bridge Knots and Links by : Jerome Minkus

Download or read book The Branched Cyclic Coverings of 2 Bridge Knots and Links written by Jerome Minkus and published by American Mathematical Soc.. This book was released on 1982 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper a family of closed oriented 3 dimensional manifolds {[italic]M[subscript italic]n([italic]k,[italic]h)} is constructed by pasting together pairs of regions on the boundary of a 3 ball. The manifold [italic]M[subscript italic]n([italic]k,[italic]h) is a generalization of the lens space [italic]L([italic]n,1) and is closely related to the 2 bridge knot or link of type ([italic]k,[italic]h). While the work is basically geometrical, examination of [lowercase Greek]Pi1([italic]M[subscript italic]n([italic]k,[italic]h)) leads naturally to the study of "cyclic" presentations of groups. Abelianizing these presentations gives rise to a formula for the Alexander polynomials of 2 bridge knots and to a description of [italic]H1([italic]M[subscript italic]n([italic]k,[italic]h), [italic]Z) by means of circulant matrices whose entries are the coefficients of these polynomials.

Real and Complex Singularities

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Publisher : Springer Science & Business Media
ISBN 13 : 3764377763
Total Pages : 363 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Real and Complex Singularities by : Jean-Paul Brasselet

Download or read book Real and Complex Singularities written by Jean-Paul Brasselet and published by Springer Science & Business Media. This book was released on 2007-01-05 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects papers presented at the eighth São Carlos Workshop on Real and Complex Singularities, held at the IML, Marseille, July 2004. Like the workshop, this collection establishes the state of the art and presents new trends, new ideas and new results in all of the branches of singularities. Real and Complex Singularities offers a useful summary of leading ideas in singularity theory, and inspiration for future research.

Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88

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Publisher : Princeton University Press
ISBN 13 : 1400881501
Total Pages : 368 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88 by : Robion C. Kirby

Download or read book Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88 written by Robion C. Kirby and published by Princeton University Press. This book was released on 2016-03-02 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area. The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.

Volume Conjecture for Knots

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Publisher : Springer
ISBN 13 : 9811311501
Total Pages : 126 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Volume Conjecture for Knots by : Hitoshi Murakami

Download or read book Volume Conjecture for Knots written by Hitoshi Murakami and published by Springer. This book was released on 2018-08-15 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume conjecture states that a certain limit of the colored Jones polynomial of a knot in the three-dimensional sphere would give the volume of the knot complement. Here the colored Jones polynomial is a generalization of the celebrated Jones polynomial and is defined by using a so-called R-matrix that is associated with the N-dimensional representation of the Lie algebra sl(2;C). The volume conjecture was first stated by R. Kashaev in terms of his own invariant defined by using the quantum dilogarithm. Later H. Murakami and J. Murakami proved that Kashaev’s invariant is nothing but the N-dimensional colored Jones polynomial evaluated at the Nth root of unity. Then the volume conjecture turns out to be a conjecture that relates an algebraic object, the colored Jones polynomial, with a geometric object, the volume. In this book we start with the definition of the colored Jones polynomial by using braid presentations of knots. Then we state the volume conjecture and give a very elementary proof of the conjecture for the figure-eight knot following T. Ekholm. We then give a rough idea of the “proof”, that is, we show why we think the conjecture is true at least in the case of hyperbolic knots by showing how the summation formula for the colored Jones polynomial “looks like” the hyperbolicity equations of the knot complement. We also describe a generalization of the volume conjecture that corresponds to a deformation of the complete hyperbolic structure of a knot complement. This generalization would relate the colored Jones polynomial of a knot to the volume and the Chern–Simons invariant of a certain representation of the fundamental group of the knot complement to the Lie group SL(2;C). We finish by mentioning further generalizations of the volume conjecture.

Dynamics of Discrete Group Action

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110784130
Total Pages : 714 pages
Book Rating : 4.1/5 (17 download)

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Book Synopsis Dynamics of Discrete Group Action by : Boris N. Apanasov

Download or read book Dynamics of Discrete Group Action written by Boris N. Apanasov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-07-22 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides the first systematic study of geometry and topology of locally symmetric rank one manifolds and dynamics of discrete action of their fundamental groups. In addition to geometry and topology, this study involves several other areas of Mathematics – from algebra of varieties of groups representations and geometric group theory, to geometric analysis including classical questions from function theory.

Infinite Loop Spaces (AM-90), Volume 90

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Publisher : Princeton University Press
ISBN 13 : 1400821258
Total Pages : 230 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Infinite Loop Spaces (AM-90), Volume 90 by : John Frank Adams

Download or read book Infinite Loop Spaces (AM-90), Volume 90 written by John Frank Adams and published by Princeton University Press. This book was released on 1978-09-01 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of infinite loop spaces has been the center of much recent activity in algebraic topology. Frank Adams surveys this extensive work for researchers and students. Among the major topics covered are generalized cohomology theories and spectra; infinite-loop space machines in the sense of Boadman-Vogt, May, and Segal; localization and group completion; the transfer; the Adams conjecture and several proofs of it; and the recent theories of Adams and Priddy and of Madsen, Snaith, and Tornehave.

Pseudo-periodic Maps and Degeneration of Riemann Surfaces

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Publisher : Springer
ISBN 13 : 3642225349
Total Pages : 251 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Pseudo-periodic Maps and Degeneration of Riemann Surfaces by : Yukio Matsumoto

Download or read book Pseudo-periodic Maps and Degeneration of Riemann Surfaces written by Yukio Matsumoto and published by Springer. This book was released on 2011-08-17 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen's incomplete classification is corrected. The second part applies the results of the first part to the topology of degeneration of Riemann surfaces. It is shown that the set of topological types of all the singular fibers appearing in one parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of negative twists. The correspondence is given by the topological monodromy.

Prospects in Topology (AM-138), Volume 138

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Publisher : Princeton University Press
ISBN 13 : 1400882583
Total Pages : 357 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Prospects in Topology (AM-138), Volume 138 by : Frank Quinn

Download or read book Prospects in Topology (AM-138), Volume 138 written by Frank Quinn and published by Princeton University Press. This book was released on 2016-03-02 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection brings together influential papers by mathematicians exploring the research frontiers of topology, one of the most important developments of modern mathematics. The papers cover a wide range of topological specialties, including tools for the analysis of group actions on manifolds, calculations of algebraic K-theory, a result on analytic structures on Lie group actions, a presentation of the significance of Dirac operators in smoothing theory, a discussion of the stable topology of 4-manifolds, an answer to the famous question about symmetries of simply connected manifolds, and a fresh perspective on the topological classification of linear transformations. The contributors include A. Adem, A. H. Assadi, M. Bökstedt, S. E. Cappell, R. Charney, M. W. Davis, P. J. Eccles, M. H. Freedman, I. Hambleton, J. C. Hausmann, S. Illman, G. Katz, M. Kreck, W. Lück, I. Madsen, R. J. Milgram, J. Morava, E. K. Pedersen, V. Puppe, F. Quinn, A. Ranicki, J. L. Shaneson, D. Sullivan, P. Teichner, Z. Wang, and S. Weinberger.

On Knots. (AM-115), Volume 115

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Publisher : Princeton University Press
ISBN 13 : 1400882133
Total Pages : 498 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis On Knots. (AM-115), Volume 115 by : Louis H. Kauffman

Download or read book On Knots. (AM-115), Volume 115 written by Louis H. Kauffman and published by Princeton University Press. This book was released on 2016-03-02 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: On Knots is a journey through the theory of knots, starting from the simplest combinatorial ideas--ideas arising from the representation of weaving patterns. From this beginning, topological invariants are constructed directly: first linking numbers, then the Conway polynomial and skein theory. This paves the way for later discussion of the recently discovered Jones and generalized polynomials. The central chapter, Chapter Six, is a miscellany of topics and recreations. Here the reader will find the quaternions and the belt trick, a devilish rope trick, Alhambra mosaics, Fibonacci trees, the topology of DNA, and the author's geometric interpretation of the generalized Jones Polynomial. Then come branched covering spaces, the Alexander polynomial, signature theorems, the work of Casson and Gordon on slice knots, and a chapter on knots and algebraic singularities.The book concludes with an appendix about generalized polynomials.

Ricci Flow and Geometric Applications

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Publisher : Springer
ISBN 13 : 3319423517
Total Pages : 149 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Ricci Flow and Geometric Applications by : Michel Boileau

Download or read book Ricci Flow and Geometric Applications written by Michel Boileau and published by Springer. This book was released on 2016-09-09 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting some impressive recent achievements in differential geometry and topology, this volume focuses on results obtained using techniques based on Ricci flow. These ideas are at the core of the study of differentiable manifolds. Several very important open problems and conjectures come from this area and the techniques described herein are used to face and solve some of them. The book’s four chapters are based on lectures given by leading researchers in the field of geometric analysis and low-dimensional geometry/topology, respectively offering an introduction to: the differentiable sphere theorem (G. Besson), the geometrization of 3-manifolds (M. Boileau), the singularities of 3-dimensional Ricci flows (C. Sinestrari), and Kähler–Ricci flow (G. Tian). The lectures will be particularly valuable to young researchers interested in differential manifolds.

Canadian Journal of Mathematics

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Publisher :
ISBN 13 :
Total Pages : 260 pages
Book Rating : 4./5 ( download)

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Book Synopsis Canadian Journal of Mathematics by :

Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1981-04 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Knots and Primes

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Publisher : Springer Nature
ISBN 13 : 9819992559
Total Pages : 268 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis Knots and Primes by : Masanori Morishita

Download or read book Knots and Primes written by Masanori Morishita and published by Springer Nature. This book was released on with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:

At the Frontier of Spacetime

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Publisher : Springer
ISBN 13 : 3319312995
Total Pages : 326 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis At the Frontier of Spacetime by : Torsten Asselmeyer-Maluga

Download or read book At the Frontier of Spacetime written by Torsten Asselmeyer-Maluga and published by Springer. This book was released on 2016-04-28 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, leading theorists present new contributions and reviews addressing longstanding challenges and ongoing progress in spacetime physics. In the anniversary year of Einstein's General Theory of Relativity, developed 100 years ago, this collection reflects the subsequent and continuing fruitful development of spacetime theories. The volume is published in honour of Carl Brans on the occasion of his 80th birthday. Carl H. Brans, who also contributes personally, is a creative and independent researcher and one of the founders of the scalar-tensor theory, also known as Jordan-Brans-Dicke theory. In the present book, much space is devoted to scalar-tensor theories. Since the beginning of the 1990s, Brans has worked on new models of spacetime, collectively known as exotic smoothness, a field largely established by him. In this Festschrift, one finds an outstanding and unique collection of articles about exotic smoothness. Also featured are Bell's inequality and Mach's principle. Personal memories and historical aspects round off the collection.

The Arithmetic of Hyperbolic 3-Manifolds

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Publisher : Springer Science & Business Media
ISBN 13 : 147576720X
Total Pages : 472 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis The Arithmetic of Hyperbolic 3-Manifolds by : Colin Maclachlan

Download or read book The Arithmetic of Hyperbolic 3-Manifolds written by Colin Maclachlan and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Princeton Conference Series

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Publisher :
ISBN 13 :
Total Pages : 104 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Princeton Conference Series by :

Download or read book Princeton Conference Series written by and published by . This book was released on 1963 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: