ISBN-10:
0821829661
ISBN-13:
9780821829660
Pub. Date:
11/01/2001
Publisher:
American Mathematical Society
Knots, Braids, and Mapping Class Groups: Papers Dedicated to Joan S. Birman: Proceedings of a Conference on Low Dimensional Topology in Honor of Joan S. Birman's 70th Birthday, March 14-15, 1998, Columbia University, New York, New York

Knots, Braids, and Mapping Class Groups: Papers Dedicated to Joan S. Birman: Proceedings of a Conference on Low Dimensional Topology in Honor of Joan S. Birman's 70th Birthday, March 14-15, 1998, Columbia University, New York, New York

Paperback

Current price is , Original price is $44.0. You
Select a Purchase Option
  • purchase options

Overview

Knots, Braids, and Mapping Class Groups: Papers Dedicated to Joan S. Birman: Proceedings of a Conference on Low Dimensional Topology in Honor of Joan S. Birman's 70th Birthday, March 14-15, 1998, Columbia University, New York, New York

There are a number of specialties in low-dimensional topology that can find in their ''family tree'' a common ancestry in the theory of surface mappings. These include knot theory as studied through the use of braid representations and 3-manifolds as studied through the use of Heegaard splittings. The study of the surface mapping class group (the modular group) is of course a rich subject in its own right, with relations to many different fields of mathematics and theoretical physics. But its most direct and remarkable manifestation is probably in the vast area of low-dimensional topology. Although the scene of this area has been changed dramatically and experienced significant expansion since the original publication of Professor Joan Birman's seminal work, Braids, Links, and Mapping Class Groups (Princeton University Press), she brought together mathematicians whose research span many specialties, all of common lineage. The topics covered are quite diverse. Yet they reflect well the aim and spirit of the conference in low-dimensional topology held in honor of Joan S.Birman's 70th birthday at Columbia University (New York, NY), which was to explore how these various specialties in low-dimensional topology have diverged in the past 20-25 years, as well as to explore common threads and potential future directions of development.

Product Details

ISBN-13: 9780821829660
Publisher: American Mathematical Society
Publication date: 11/01/2001
Series: AMS/IP Studies in Advanced Mathematics Series , #24
Pages: 176
Product dimensions: 7.09(w) x 9.45(h) x (d)

Table of Contents

Prefaceix
Joan S. Birman: Publications and Ph.D. Theses Supervisedxiii
Photosxvii
Upper Bounds for the Writhing of Knots and the Helicity of Vector Fields1
The Automorphism Group of a Free Group is not Subgroup Separable23
Configuration Spaces and Braid Groups on Graphs in Robotics29
Alternate Discreteness Tests41
Intersection-number Operators for Curves on Discs and Chebyshev Polynomials49
Implicit Function Theorem over Free Groups and Genus Problem77
On the z-Degree of the Kauffman Polynomial of a Tangle Decomposition85
Knot Invariants from Counting Periodic Points95
Random Walk on Knot Diagrams, Colored Jones Polynomial and Ihara-Selberg Zeta Function107
Some Applications of a Multiplicative Structure on Simple Loops in Surfaces123
Closed Braids and Heegaard Splittings131
Homotopy and q-Homotopy Skein Modules of 3-Manifolds: An Example in Algebra Situs143
On Knot Invariants which are not of Finite Type171

Customer Reviews

Most Helpful Customer Reviews

See All Customer Reviews