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.
By: Jane Gilman (author), Xiao-Song Lin (author), W. Menasco (author)Paperback
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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 specialities, 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.
Upper bounds for the writhing of knots and the helicity of vector fields by J. Cantarella, D. DeTurck, and H. Gluck The automorphism group of a free group is not subgroup separable by O. T. Dasbach and B. S. Mangum Configuration spaces and braid groups on graphs in robotics by R. Ghrist Alternate discreteness tests by J. Gilman Intersection-number operators for curves on discs and Chebyshev polynomials by S. P. Humphries Implicit function theorem over free groups and genus problem by O. Kharlampovich and A. Myasnikov On the $z$-degree of the Kauffman polynomial of a tangle decomposition by M. E. Kidwell and T. B. Stanford Knot invariants from counting periodic points by W. Li Random walk on knot diagrams, colored Jones polynomial and Ihara-Selberg zeta function by X.-S. Lin and Z. Wang Some applications of a multiplicative structure on simple loops in surfaces by F. Luo Closed braids and Heegaard splittings by W. W. Menasco Homotopy and q-homotopy skein modules of 3-manifolds: An example in algebra Situs by J. H. Przytycki On knot invariants which are not of finite type by T. Stanford and R. Trapp.
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