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Author: Tim D. Cochran Publisher: American Mathematical Soc. ISBN: 9780821824894 Category : Mathematics Languages : en Pages : 102
Book Description
We investigate higher-order cohomology operations (Massey products) on complements of links of circles in [italic]S3. These are known to be essentially equivalent to the [lowercase Greek]Mu [with macron]-invariants of John Milnor, which detect whether or not the longitudes of the link lie in the [italic]n[superscript]th term of the lower central series of the fundamental group of the link compliment. We define a geometric "derivative" on the set of all links and use this to define higher-order linking numbers which are shown to be "pieces" of Massey products.
Author: Tim D. Cochran Publisher: American Mathematical Soc. ISBN: 9780821824894 Category : Mathematics Languages : en Pages : 102
Book Description
We investigate higher-order cohomology operations (Massey products) on complements of links of circles in [italic]S3. These are known to be essentially equivalent to the [lowercase Greek]Mu [with macron]-invariants of John Milnor, which detect whether or not the longitudes of the link lie in the [italic]n[superscript]th term of the lower central series of the fundamental group of the link compliment. We define a geometric "derivative" on the set of all links and use this to define higher-order linking numbers which are shown to be "pieces" of Massey products.
Author: Colin Adams Publisher: CRC Press ISBN: 1000222381 Category : Education Languages : en Pages : 954
Book Description
"Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject." – Ed Witten, Recipient of the Fields Medal "I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It’s a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field." – Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis Knot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications. Many of the articles in this book are accessible to undergraduates who are working on research or taking an advanced undergraduate course in knot theory. More advanced articles will be useful to graduate students working on a related thesis topic, to researchers in another area of topology who are interested in current results in knot theory, and to scientists who study the topology and geometry of biopolymers. Features Provides material that is useful and accessible to undergraduates, postgraduates, and full-time researchers Topics discussed provide an excellent catalyst for students to explore meaningful research and gain confidence and commitment to pursuing advanced degrees Edited and contributed by top researchers in the field of knot theory
Author: Hanna Nencka Publisher: American Mathematical Soc. ISBN: 0821808842 Category : Mathematics Languages : en Pages : 266
Book Description
"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.
Author: Akio Kawauchi Publisher: Birkhäuser ISBN: 3034892276 Category : Mathematics Languages : en Pages : 431
Book Description
Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory.
Author: Anatoly M. Vershik Publisher: American Mathematical Soc. ISBN: 1470456648 Category : Education Languages : en Pages : 345
Book Description
Vladimir Abramovich Rokhlin (8/23/1919–12/03/1984) was one of the leading Russian mathematicians of the second part of the twentieth century. His main achievements were in algebraic topology, real algebraic geometry, and ergodic theory. The volume contains the proceedings of the Conference on Topology, Geometry, and Dynamics: V. A. Rokhlin-100, held from August 19–23, 2019, at The Euler International Mathematics Institute and the Steklov Institute of Mathematics, St. Petersburg, Russia. The articles deal with topology of manifolds, theory of cobordisms, knot theory, geometry of real algebraic manifolds and dynamical systems and related topics. The book also contains Rokhlin's biography supplemented with copies of actual very interesting documents.
Author: Erica Flapan Publisher: American Mathematical Soc. ISBN: 1470428474 Category : Combinatorics -- Graph theory -- Planar graphs Languages : en Pages : 189
Book Description
This volume contains the proceedings of the AMS Special Session on Algebraic and Combinatorial Structures in Knot Theory and the AMS Special Session on Spatial Graphs, both held from October 24–25, 2015, at California State University, Fullerton, CA. Included in this volume are articles that draw on techniques from geometry and algebra to address topological problems about knot theory and spatial graph theory, and their combinatorial generalizations to equivalence classes of diagrams that are preserved under a set of Reidemeister-type moves. The interconnections of these areas and their connections within the broader field of topology are illustrated by articles about knots and links in spatial graphs and symmetries of spatial graphs in and other 3-manifolds.
Author: Akio Kawauchi Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110875918 Category : Mathematics Languages : en Pages : 652
Book Description
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Author: J. Scott Carter Publisher: World Scientific ISBN: 9812770968 Category : Mathematics Languages : en Pages : 398
Book Description
This volume gathers the contributions from the international conference Intelligence of Low Dimensional Topology 2006, which took place in Hiroshima in 2006. The aim of this volume is to promote research in low dimensional topology with the focus on knot theory and related topics. The papers include comprehensive reviews and some latest results.
Author: Tim D. Cochran
Author: Tim D. Cochran
Author: Tim D. Cochran
Author: Colin Adams
Author: Hanna Nencka
Author: Akio Kawauchi
Author: Anatoly M. Vershik
Author: Erica Flapan
Author: Akio Kawauchi
Author: J. Scott Carter
Author: Stefan Behrens