AMS/IP Studies in Advanced Mathematics 2002; 176 pp; softcover Volume: 24 ISBN10: 0821829661 ISBN13: 9780821829660 List Price: US$41 Member Price: US$32.80 Order Code: AMSIP/24
See also: Ordering Braids  Patrick Dehornoy, Ivan Dynnikov, Dale Rolfsen and Bert Wiest  There are a number of specialties in lowdimensional 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 3manifolds 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 lowdimensional 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 lowdimensional 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 lowdimensional topology have diverged in the past 2025 years, as well as to explore common threads and potential future directions of development. Titles in this series are copublished with International Press, Cambridge, MA. Readership Graduate students and research mathematicians interested in geometry and topology. Table of Contents  J. Cantarella, D. DeTurck, and H. Gluck  Upper bounds for the writhing of knots and the helicity of vector fields
 O. T. Dasbach and B. S. Mangum  The automorphism group of a free group is not subgroup separable
 R. Ghrist  Configuration spaces and braid groups on graphs in robotics
 J. Gilman  Alternate discreteness tests
 S. P. Humphries  Intersectionnumber operators for curves on discs and Chebyshev polynomials
 O. Kharlampovich and A. Myasnikov  Implicit function theorem over free groups and genus problem
 M. E. Kidwell and T. B. Stanford  On the \(z\)degree of the Kauffman polynomial of a tangle decomposition
 W. Li  Knot invariants from counting periodic points
 X.S. Lin and Z. Wang  Random walk on knot diagrams, colored Jones polynomial and IharaSelberg zeta function
 F. Luo  Some applications of a multiplicative structure on simple loops in surfaces
 W. W. Menasco  Closed braids and Heegaard splittings
 J. H. Przytycki  Homotopy and qhomotopy skein modules of 3manifolds: An example in algebra Situs
 T. Stanford and R. Trapp  On knot invariants which are not of finite type
