Computing boundary slopes of 2-bridge links
HTML articles powered by AMS MathViewer
- by Jim Hoste and Patrick D. Shanahan PDF
- Math. Comp. 76 (2007), 1521-1545 Request permission
Abstract:
We describe an algorithm for computing boundary slopes of 2-bridge links. As an example, we work out the slopes of the links obtained by $1/k$ surgery on one component of the Borromean rings. A table of all boundary slopes of all 2-bridge links with 10 or less crossings is also included.References
- Gerhard Burde and Heiner Zieschang, Knots, 2nd ed., De Gruyter Studies in Mathematics, vol. 5, Walter de Gruyter & Co., Berlin, 2003. MR 1959408
- Marc Culler and Peter B. Shalen, Varieties of group representations and splittings of $3$-manifolds, Ann. of Math. (2) 117 (1983), no. 1, 109–146. MR 683804, DOI 10.2307/2006973
- Nathan M. Dunfield, A table of boundary slopes of Montesinos knots, Topology 40 (2001), no. 2, 309–315. MR 1808223, DOI 10.1016/S0040-9383(99)00064-6
- W. Floyd and A. Hatcher, The space of incompressible surfaces in a $2$-bridge link complement, Trans. Amer. Math. Soc. 305 (1988), no. 2, 575–599. MR 924770, DOI 10.1090/S0002-9947-1988-0924770-8
- Ronald L. Graham, Donald E. Knuth, and Oren Patashnik, Concrete mathematics, 2nd ed., Addison-Wesley Publishing Company, Reading, MA, 1994. A foundation for computer science. MR 1397498
- A. Hatcher and U. Oertel, Boundary slopes for Montesinos knots, Topology 28 (1989), no. 4, 453–480. MR 1030987, DOI 10.1016/0040-9383(89)90005-0
- A. Hatcher and W. Thurston, Incompressible surfaces in $2$-bridge knot complements, Invent. Math. 79 (1985), no. 2, 225–246. MR 778125, DOI 10.1007/BF01388971
- Jim Hoste and Morwen Thistlethwaite. Knotscape. http://www.math.utk.edu/~morwen, 1998.
- Alan E. Lash. Boundary curve space of the Whitehead link complement. Ph.D. thesis, University of California, Santa Barbara, 1993.
- Tomotada Ohtsuki, Ideal points and incompressible surfaces in two-bridge knot complements, J. Math. Soc. Japan 46 (1994), no. 1, 51–87. MR 1248091, DOI 10.2969/jmsj/04610051
- Dale Rolfsen, Knots and links, Mathematics Lecture Series, vol. 7, Publish or Perish, Inc., Houston, TX, 1990. Corrected reprint of the 1976 original. MR 1277811
Additional Information
- Jim Hoste
- Affiliation: Pitzer College, 1050 N. Mills Ave., Claremont, California 91711
- MR Author ID: 88610
- Email: jhoste@pitzer.edu
- Patrick D. Shanahan
- Affiliation: Loyola Marymount University, 1 LMU Dr., Los Angeles, California 90045-2659
- MR Author ID: 537475
- Email: pshanahan@lmu.edu
- Received by editor(s): May 24, 2005
- Received by editor(s) in revised form: March 31, 2006
- Published electronically: March 12, 2007
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 76 (2007), 1521-1545
- MSC (2000): Primary 57M25
- DOI: https://doi.org/10.1090/S0025-5718-07-01936-9
- MathSciNet review: 2299787