Selected Title s i n Thi s Serie s 24 Jan e Gilman , Willia m W . Menasco , an d Xiao-Son g Lin , Editors , Knots , Braids , and Mappin g Clas s Groups—Paper s Dedicate d t o Joa n S . Birman, 200 1 23 Cumru n Vaf a an d S.-T . Yau , Editors , Winte r Schoo l o n Mirro r Symmetry , Vecto r Bundles an d Lagrangia n Submanifolds , 200 1 22 Carlo s Berenstein , Der-Che n Chang , an d Jingzh i Tie , Laguerr e Calculu s an d It s Applications o n the Heisenber g Group , 200 1 21 Jiirge n Jost , Bosoni c Strings : A Mathematical Treatment , 200 1 20 L o Yan g an d S.-T . Yau , Editors , Firs t Internationa l Congres s o f Chines e Mathematicians, 200 1 19 So-Chi n Che n an d Mei-Ch i Shaw , Partia l Differentia l Equation s i n Severa l Comple x Variables, 200 1 18 Fangyan g Zheng , Comple x Differentia l Geometry , 200 0 17 Le i Gu o an d Stephe n S.-T . Yau , Editors , Lecture s o n Systems , Control , an d Information, 200 0 16 Rud i Weikar d an d Gilber t Weinstein , Editors , Differentia l Equation s an d Mathematical Physics , 200 0 15 Lin g Hsia o an d Zhoupin g Xin , Editors , Som e Curren t Topic s o n Nonlinea r Conservation Laws , 200 0 14 Jun-ich i Igusa , A n Introductio n t o the Theor y o f Loca l Zet a Functions , 200 0 13 Vasilio s Alexiade s an d Georg e Siopsis , Editors , Trend s i n Mathematica l Physics , 1999 12 Shen g Gong , Th e Bieberbac h Conjecture , 199 9 11 Shinich i Mochizuki , Foundation s o f p-adic Teichmulle r Theory , 199 9 10 Duon g H . Phong , Lu c Vinet , an d Shing-Tun g Yau , Editors , Mirro r Symmetr y III , 1999 9 Shing-Tun g Yau , Editor , Mirro r Symmetr y I , 199 8 8 Jiirge n Jost , Wilfri d Kendall , Umbert o Mosco , Michae l Rockner , and Karl-Theodo r Sturm , Ne w Direction s i n Dirichle t Forms , 199 8 7 D . A . Buel l an d J . T . Teitelbaum , Editors , Computationa l Perspective s o n Numbe r Theory, 199 8 6 Harol d Levine , Partia l Differentia l Equations , 199 7 5 Qi-ken g Lu , Stephe n S.-T . Yau , an d Anatol y Libgober , Editors , Singularitie s an d Complex Geometry , 199 7 4 Vyjayanth i Char i an d Iva n B . Penkov , Editors , Modula r Interfaces : Modula r Li e Algebras, Quantu m Groups , an d Li e Superalgebras, 199 7 3 Xia-X i Din g an d Tai-Pin g Liu , Editors , Nonlinea r Evolutionar y Partia l Differentia l Equations, 199 7 2.2 Willia m H . Kazez , Editor , Geometri c Topology , 199 7 2.1 Willia m H . Kazez , Editor , Geometri c Topology , 199 7 1 B . Green e an d S.-T . Yau , Editors , Mirro r Symmetr y II , 199 7 This page intentionally left blank Knots, Braids, and Mappin g Class Groups—Papers Dedicate d to Joan S . Birman This page intentionally left blank https://doi.org/10.1090/amsip/024 AMS/IP Studies in Advanced Mathematics Volume 24 Knots, Braids, and Mappin g Class Groups—Papers Dedicate d to Joan S . Birman Proceedings o f a Conferenc e in Low Dimensional Topolog y in Honor o f Joan S . Birman's 70t h Birthda y March 14-15 , 199 8 Columbia Universit y New York, New York Jane Gilman, William W. Menasco, and Xiao-Song Lin, Editors American Mathematical Society • International Press Shing-Tung Yau , Genera l Edito r 2000 Mathematics Subject Classification. Primar y 42C40 . Library o f Congres s Cataloging-in-Publicatio n Dat a Knots, braids , an d mappin g clas s groups—paper s dedicate d t o Joa n S . Birma n : proceeding s o f a conferenc e o n lo w dimensiona l topolog y i n hono r o f Joa n S . Birman' s 70t h birthday , Marc h 14-15, 1998 , Columbi a University , Ne w York , Ne w Yor k / Jan e Gilman , Willia m W . Menasco , and Xiao-Son g Lin , editors . p. cm . — (AMS/I P studie s i n advance d mathematics , ISS N 1089-328 8 ; v. 24 ) Includes bibliographica l references . ISBN 0-8218-2966- 1 (alk . paper ) 1. Lo w dimensiona l topology—Congresses . I . Birman , Joa n S. , 1927 - II . Gilman , Jane , 1945- III . Menasco , Willia m W. , 1954 - IV . Lin , Xiao-Song , 1957 - V . Series . QA612.14.K58 200 1 514'.22—dc21 2001053661 Copying an d reprinting . Materia l i n thi s boo k ma y b e reproduce d b y an y mean s fo r edu - cational an d scientifi c purpose s withou t fe e o r permissio n wit h th e exceptio n o f reproductio n b y services that collec t fee s fo r deliver y o f documents an d provide d tha t th e customar y acknowledg - ment o f the sourc e i s given . Thi s consen t doe s no t exten d t o othe r kind s o f copyin g fo r genera l distribution, fo r advertisin g o r promotiona l purposes , o r fo r resale . Request s fo r permissio n fo r commercial us e o f materia l shoul d b e addresse d t o th e Assistan t t o th e Publisher , America n Mathematical Society , P . O. Bo x 6248 , Providence , Rhod e Islan d 02940-6248 . Request s ca n axs o be mad e b y e-mai l t o [email protected] . Excluded fro m thes e provision s i s material i n article s fo r whic h the autho r hold s copyright. I n such cases , requests fo r permissio n t o us e o r reprint shoul d b e addresse d directl y to the author(s) . (Copyright ownershi p i s indicated i n the notic e i n the lowe r right-han d corne r o f the firs t pag e o f each article. ) © 200 1 b y the America n Mathematica l Societ y an d Internationa l Press . Al l rights reserved . The America n Mathematica l Societ y an d Internationa l Pres s retai n al l right s except thos e grante d t o th e Unite d State s Government . Printed i n the Unite d State s o f America . @ Th e pape r use d i n thi s boo k i s acid-fre e an d fall s withi n th e guideline s established t o ensur e permanenc e an d durability . Visit th e AM S hom e pag e a t URL : http://www.ams.org / Visit th e Internationa l Pres s hom e pag e a t URL : http://www.intlpress.com / 10 9 8 7 6 5 4 3 2 1 0 6 0 5 0 4 0 3 0 2 0 1 Table o f Contents Preface i x Joan S . Birman: Publication s an d Ph.D . These s Supervise d xii i Photos xvi i J. Cantarella , D . DeTurck, an d H . Gluck , Upper Bounds for the Writhing of Knots and the Helicity of Vector Fields 1 O.T. Dasbac h an d B.S . Mangum, The Automorphism Group of a Free Group is not Subgroup Separable 2 3 R. Ghrist , Configuration Spaces and Braid Groups on Graphs in Robotics . 29 J. Gilman , Alternate Discreteness Tests 4 1 S.P. Humphries , Intersection-number Operators for Curves on Discs and Chebyshev Polynomials 4 9 O. Kharlampovich an d A . Myasnikov , Implicit Function Theorem over Free Groups and Genus Problem 7 7 M.E. Kidwel l an d T.B . Stanford , On the z-Degree of the Kauffman Polynomial of a Tangle Decomposition 8 5 W. Li , Knot Invariants from Counting Periodic Points 9 5 X.-S. Li n an d Z . Wang, Random Walk on Knot Diagrams, Colored Jones Polynomial and Ihara-Selberg Zeta Function 10 7 F. Luo , Some Applications of a Multiplicative Structure on Simple Loops in Surfaces 12 3 W.W. Menasco , Closed Braids and Heegaard Splittings 13 1 J.H. Przytycki , Homotopy and q-Homotopy Skein Modules of 3-Manifolds: An Example in Algebra Situs 14 3 T.B. Stanfor d an d R . Trapp , On Knot Invariants which are not of Finite Type 17 1 vii This page intentionally left blank Preface On Marc h 1 4 & 15 , 1998 , a conferenc e i n low-dimensiona l topolog y i n hono r of Professor Joa n Birman' s 70t h birthday wa s held i n Columbi a Universit y i n Ne w York City . Th e organizin g committe e o f tha t conferenc e consiste d o f Vladimi r Arnold, Dav e Bayer, Elizabeth Finkelstein , Rober t Friedma n (chair) , Jane Gilman , Vaughan Jones , Xiao-Son g Lin , Bria n Mangum , an d Willia m Menasco . A gran t from NSF gave partial support fo r the conference. Th e warm hospitality o f Barnard College an d th e Mathematic s Departmen t o f Columbi a Universit y a s wel l a s th e talks given by Colin Adams, Robert Ghrist, Vaughan Jones, Xiao-Song Lin, William Menasco, Joze f Przytyski , Carolin e Series , and Arkad y Vaintro b mad e this confer - ence a memorable even t fo r it s on e hundred plu s participants .