Volume: 24; 2002; 176 pp; Softcover
MSC: Primary 42;
Print ISBN: 978-0-8218-2966-0
Product Code: AMSIP/24
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Electronic ISBN: 978-1-4704-3814-2
Product Code: AMSIP/24.E
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Knots, Braids, and Mapping Class Groups—Papers Dedicated to Joan S. Birman
Share this pageEdited by Jane Gilman; William W. Menasco; Xiao-Song Lin
A co-publication of the AMS and International Press of Boston
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.
Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.
Readership
Graduate students and research mathematicians interested in geometry and topology.
Table of Contents
Knots, Braids, and Mapping Class Groups -- Papers Dedicated to Joan S. Birman
- Cover Cover11
- Title page v6
- Contents vii8
- Preface ix10
- Publications xiii14
- Photo section xvii18
- Upper bounds for the writhing of knots and the helicity of vector fields 124
- The automorphism group of a free group is not subgroup separable 2346
- Configuration spaces and braid groups on graphs in robotics 2952
- Alternate discreteness tests 4164
- Intersection-number operators for curves on discs and Chebyshev polynomials 4972
- Implicit function theorem over free groups and genus problem 77100
- On the 𝑧-degree of the Kauffman polynomial of a tangle decomposition 85108
- Knot invariants from counting periodic points 95118
- Random walk on knot diagrams, colored Jones polynomial and Ihara-Selberg zeta function 107130
- Some applications of a multiplicative structure on simple loops in surfaces 123146
- Closed braids and Heegaard splittings 131154
- Homotopy and q-homotopy skein modules of 3-manifolds: An example in algebra Situs 143166
- On knot invariants which are not of finite type 171194
- Back Cover Back Cover1200