Low Dimensional Topology

Author: Samuel J. Lomonaco

Publisher: American Mathematical Soc.

ISBN: 0821850164

Category: Mathematics

Page: 346

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This volume arose from a special session on Low Dimensional Topology organized and conducted by Dr. Lomonaco at the American Mathematical Society meeting held in San Francisco, California, January 7-11, 1981.

Algebraic Topology and Related Topics

Author: Mahender Singh,Yongjin Song,Jie Wu

Publisher: Springer

ISBN: 9811357420

Category: Mathematics

Page: 313

View: 539

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This book highlights the latest advances in algebraic topology, from homotopy theory, braid groups, configuration spaces and toric topology, to transformation groups and the adjoining area of knot theory. It consists of well-written original research papers and survey articles by subject experts, most of which were presented at the “7th East Asian Conference on Algebraic Topology” held at the Indian Institute of Science Education and Research (IISER), Mohali, Punjab, India, from December 1 to 6, 2017. Algebraic topology is a broad area of mathematics that has seen enormous developments over the past decade, and as such this book is a valuable resource for graduate students and researchers working in the field.

Algebraic Invariants of Links

Author: Jonathan Arthur Hillman

Publisher: World Scientific

ISBN: 9814407399

Category: Mathematics

Page: 353

View: 3348

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This book serves as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors. It emphasizes the features of the multicomponent case not normally considered by knot-theorists, such as longitudes, the homological complexity of many-variable Laurent polynomial rings, the fact that links are not usually boundary links, free coverings of homology boundary links, the lower central series as a source of invariants, nilpotent completion and algebraic closure of the link group, and disc links. Invariants of the types considered here play an essential role in many applications of knot theory to other areas of topology. This second edition introduces two new chapters OCo twisted polynomial invariants and singularities of plane curves. Each replaces brief sketches in the first edition. Chapter 2 has been reorganized, and new material has been added to four other chapters.

Algebraic Invariants of Links

Author: Jonathan Hillman

Publisher: World Scientific

ISBN: 9814407402

Category: Mathematics

Page: 372

View: 5785

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This book serves as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors. It emphasizes the features of the multicomponent case not normally considered by knot-theorists, such as longitudes, the homological complexity of many-variable Laurent polynomial rings, the fact that links are not usually boundary links, free coverings of homology boundary links, the lower central series as a source of invariants, nilpotent completion and algebraic closure of the link group, and disc links. Invariants of the types considered here play an essential role in many applications of knot theory to other areas of topology. This second edition introduces two new chapters — twisted polynomial invariants and singularities of plane curves. Each replaces brief sketches in the first edition. Chapter 2 has been reorganized, and new material has been added to four other chapters. Sample Chapter(s) Chapter 1: Links (205 KB) Contents:Abelian Covers:LinksHomology and Duality in CoversDeterminantal InvariantsThe Maximal Abelian CoverSublinks and Other Abelian CoversTwisted Polynomial InvariantsApplications: Special Cases and Symmetries:Knot ModulesLinks with Two ComponentsSymmetriesSingularities of Plane Algebraic CurvesFree Covers, Nilpotent Quotients and Completion:Free CoversNilpotent QuotientsAlgebraic ClosureDisc Links Readership: Graduate students and academics in geometry and topology. Keywords:Algebraic Invariant;Links;Abelian Cover;Twisted Polynomial Invariant;Knot ModuleReviews: “The main change to the book is the addition of two chapters. These are timely and welcome additions to an already useful and comprehensive book.” Mathematical Reviews Reviews of the First Edition: “Jonathan Hillman has successfully filled an unfortunate gap in the literature of low-dimensional topology … With this up-to-date book we have a reference covering a range of topics that until now were available only in their original sources … Hillman has done an excellent job of referencing his book, both within the text and in the bibliography, with several hundred references included.” Mathematical Reviews “Algebraic Invariants of Links is masterful, offering a survey of work, much of which has not been summarized elsewhere. It is an essential reference for those interested in link theory … it is unique and valuable.” Bulletin of the American Mathematical Society “The author, who is one of the major experts on the topic, must be surely congratulated for this attractive book, written in a careful, very precise and quite readable style. It serves as an excellent self-contained and up-to-date monograph on the algebraic invariants of links … I strongly recommend this beautiful book to anyone interested in the algebraic theory of links and its applications.” Mathematics Abstracts

Low Dimensional Topology

Proceedings of a Conference on Low Dimensional Topology, January 12-17, 1998, Funchal, Madeira, Portugal

Author: Hanna Nencka

Publisher: American Mathematical Soc.

ISBN: 9780821808849

Category: Mathematics

Page: 249

View: 8862

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This volume presents the proceedings from the conference on low dimensional topology held at the University of Madeira (Portugal). The event was attended by leading scientists in the field from the U.S., Asia, and Europe. The book has two main parts. The first is devoted to the Poincare conjecture, characterizations of $PL$-manifolds, covering quadratic forms of links and to categories in low dimensional topology that appear in connection with conformal and quantum field theory. The second part of the volume covers topological quantum field theory and polynomial invariants for rational homology 3-spheres, derived from the quantum $SU(2)$-invariants associated with the first cohomology class modulo two, knot theory, and braid groups. This collection reflects development and progress in the field and presents interesting and new results.

Low-dimensional Topology and Kleinian Groups

Author: D. B. A. Epstein

Publisher: CUP Archive

ISBN: 9780521339056

Category: Mathematics

Page: 321

View: 8420

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Volume 2 is divided into three parts: the first 'Surfaces' contains an article by Thurston on earthquakes and by Penner on traintracks. The second part is entitled 'Knots and 3-Manifolds' and the final part 'Kleinian Groups'.

Low-dimensional topology

University of Tennessee, Knoxville, May 18-23, 1992

Author: Klaus Johannson

Publisher: Intl Pr of Boston Inc

ISBN: N.A

Category: Mathematics

Page: 239

View: 6806

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Topology and Geometry

Commemorating SISTAG : Singapore International Symposium in Topology and Geometry, (SISTAG) July 2-6, 2001, National University of Singapore, Singapore

Author: A. Jon Berrick,Man Chun Leung,Xingwang Xu,Singapore international symposium in topology and geometry,Michel Chun LeDoux,Singapore International Symposium in Topology and Geometry (2001 National University of

Publisher: American Mathematical Soc.

ISBN: 0821828207

Category: Mathematics

Page: 263

View: 5909

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This volume presents 19 refereed articles written by participants in the Singapore International Symposium in Topology and Geometry (SISTAG), held July 2-6, 2001, at the National University of Singapore. Rather than being a simple snapshot of the meeting in the form of a proceedings, it serves as a commemorative volume consisting of papers selected to show the diversity and depth of the mathematics presented at SISTAG. The book contains articles on low-dimensional topology, algebraic, differential and symplectic geometry, and algebraic topology. While papers reflect the focus of the conference, many documents written after SISTAG and included in this volume represent the most up-to-date thinking in the fields of topology and geometry. While representation from Pacific Rim countries is strong, the list of contributors is international in scope and includes many recognized experts. This volume is of interest to graduate students and mathematicians working in the fields of algebraic, differential and symplectic geometry, algebraic, geometric and low-dimensional topology, and mathematical physics.

Low dimensional topology

lectures at the Morningside Center of Mathematics

Author: Benghe Li,Shicheng Wang,Xuezhi Zhao

Publisher: Intl Pr of Boston Inc

ISBN: N.A

Category: Mathematics

Page: 77

View: 620

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Interactions Between Hyperbolic Geometry, Quantum Topology, and Number Theory

Workshop, June 3-13, 2009, Conference, June 15-19, 2009, Columbia University, New Ork, NY

Author: Abhijit Champanerkar

Publisher: American Mathematical Soc.

ISBN: 0821849603

Category: Mathematics

Page: 257

View: 5281

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This book is based on a 10-day workshop given by leading experts in hyperbolic geometry, quantum topology and number theory, in June 2009 at Columbia University. Each speaker gave a minicourse consisting of three or four lectures aimed at graduate students and recent PhDs. The proceedings of this enormously successful workshop can serve as an introduction to this active research area in a way that is expository and broadly accessible to graduate students. Although many ideas overlap, the twelve expository/research papers in this volume can be grouped into four rough categories: (1) different approaches to the Volume Conjecture, and relations between the main quantum and geometric invariants; (2) the geometry associated to triangulations of hyperbolic 3-manifolds; (3) arithmetic invariants of hyperbolic 3-manifolds; (4) quantum invariants associated to knots and hyperbolic 3-manifolds. The workshop, the conference that followed, and these proceedings continue a long tradition in quantum and geometric topology of bringing together ideas from diverse areas of mathematics and physics, and highlights the importance of collaborative research in tackling big problems that require expertise in disparate disciplines.

The Influence of Solomon Lefschetz in Geometry and Topology

50 Years of Mathematics at CINVESTAV

Author: Ernesto Lupercio, Francisco J. Turrubiates

Publisher: American Mathematical Soc.

ISBN: 0821894943

Category: Mathematics

Page: 226

View: 9608

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The influence of Solomon Lefschetz (1884-1972) in geometry and topology 40 years after his death has been very profound. Lefschetz's influence in Mexican mathematics has been even greater. In this volume, celebrating 50 years of mathematics at Cinvestav-México, many of the fields of geometry and topology are represented by some of the leaders of their respective fields. This volume opens with Michael Atiyah reminiscing about his encounters with Lefschetz and México. Topics covered in this volume include symplectic flexibility, Chern-Simons theory and the theory of classical theta functions, toric topology, the Beilinson conjecture for finite-dimensional associative algebras, partial monoids and Dold-Thom functors, the weak b-principle, orbit configuration spaces, equivariant extensions of differential forms for noncompact Lie groups, dynamical systems and categories, and the Nahm pole boundary condition.

Topics in Geometric Group Theory

Author: Pierre de la Harpe

Publisher: University of Chicago Press

ISBN: 9780226317212

Category: Mathematics

Page: 310

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In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.

Topology and Geometry in Dimension Three

Triangulations, Invariants, and Geometric Structures : Conference in Honor of William Jaco's 70th Birthday, June 4-6, 2010, Oklahoma State University, Stillwater, Oklahoma

Author: William H. Jaco

Publisher: American Mathematical Soc.

ISBN: 0821852957

Category: Mathematics

Page: 196

View: 2972

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This volume contains the proceedings of a conference held from June 4-6, 2010, at Oklahoma State University, in honor of William (Bus) Jaco's 70th birthday. His contributions to research in low dimensional geometry and topology and to the American mathematical community, especially through his work for the American Mathematical Society, were recognized during the conference. The focus of the conference was on triangulations and geometric structures for three-dimensional manifolds. The papers in this volume present significant new results on these topics, as well as in geometric group theory.

Advances in Quantum Computation

Representation Theory, Quantum Field Theory, Category Theory, Mathematical Physics, and Quantum Information Theory, September 20-23, 2007, University of Texas at Tyler

Author: Kazem Mahdavi,Deborah Koslover

Publisher: American Mathematical Soc.

ISBN: 0821846272

Category: Mathematics

Page: 240

View: 2773

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This volume represents the talks given at the Conference on Interactions between Representation Theory, Quantum Field Theory, Category Theory, Mathematical Physics, and Quantum Information Theory, held in September 2007 at the University of Texas at Tyler. The papers in this volume, written by top experts in the field, address physical aspects, mathematical aspects, and foundational issues of quantum computation. This volume will benefit researchers interested in advances in quantum computation and communication, as well as graduate students who wish to enter the field of quantum computation.

Anschauliche Geometrie

Author: David Hilbert,Stephan Cohn-Vossen

Publisher: Springer-Verlag

ISBN: 3642199488

Category: Mathematics

Page: 364

View: 8419

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1932 erstmals erschienen, hat der Klassiker der Geometrie bis heute nichts von seiner Frische und Kraft eingebüßt. Die weltbekannten Autoren stellen in dem Band zugrundeliegende Leitmotive und verblüffende Zusammenhänge in der Geometrie verständlich dar. David Hilbert, dessen Ziel es war, die Faszination der Geometrie zu vermitteln, schrieb im Vorwort: „Das Buch soll dazu dienen, die Freude an der Mathematik zu mehren, indem es dem Leser erleichtert, in das Wesen der Mathematik einzudringen, ohne sich einem beschwerlichen Studium zu unterziehen".

Geometry and Topology Down Under

Author: Craig D. Hodgson,William H. Jaco,Martin G. Scharlemann,Stephan Tillmann

Publisher: American Mathematical Soc.

ISBN: 0821884808

Category: Mathematics

Page: 369

View: 1187

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This book contains the proceedings of the conference Geometry & Topology Down Under, held July 11-22, 2011, at the University of Melbourne, Parkville, Australia, in honour of Hyam Rubinstein. The main topic of the book is low-dimensional geometry and topology. It includes both survey articles based on courses presented at the conferences and research articles devoted to important questions in low-dimensional geometry. Together, these contributions show how methods from different fields of mathematics contribute to the study of 3-manifolds and Gromov hyperbolic groups. It also contains a list of favorite problems by Hyam Rubinstein.

Differential Topology, Foliations, and Group Actions

Author: Paul A. Schweitzer

Publisher: American Mathematical Soc.

ISBN: 0821851705

Category: Mathematics

Page: 287

View: 1205

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This volume contains the proceedings of the Workshop on Topology held at the Pontificia Universidade Catolica in Rio de Janeiro in January 1992. Bringing together about one hundred mathematicians from Brazil and around the world, the workshop covered a variety of topics in differential and algebraic topology, including group actions, foliations, low-dimensional topology, and connections to differential geometry. The main concentration was on foliation theory, but there was a lively exchange on other current topics in topology. The volume contains an excellent list of open problems in foliation research, prepared with the participation of some of the top world experts in this area. Also presented here are two surveys on group actions - finite group actions and rigidity theory for Anosov actions - as well as an elementary survey of Thurston's geometric topology in dimensions 2 and 3 that would be accessible to advanced undergraduates and graduate students.