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Computing boundary slopes of 2-bridge links
Author(s):
Jim
Hoste;
Patrick
D.
Shanahan.
Journal:
Math. Comp.
76
(2007),
1521-1545.
MSC (2000):
Primary 57M25
Posted:
March 12, 2007
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Additional information
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 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:
-
- 1.
- Gerhard Burde and Heiner Zieschang.
Knots, volume 5 of de Gruyter Studies in Mathematics. Walter de Gruyter & Co., Berlin, 2003. MR 1959408 (2003m:57005) - 2.
- M. Culler and P. Shalen.
Varieties of group representations and splittings of 3-manifolds. Annals of Mathematics, 117:109-146, 1983. MR 683804 (84k:57005) - 3.
- Nathan M. Dunfield.
A table of boundary slopes of Montesinos knots. Topology, 40:309-315, 2001, arXiv:math.GT/9901120. MR 1808223 (2001j:57008) - 4.
- W. Floyd and A. Hatcher.
The space of incompressible surfaces in a -bridge link complement. Trans. Amer. Math. Soc., 305(2):575-599, 1988. MR 924770 (89c:57004) - 5.
- Ronald L. Graham, Donald E. Knuth, and Oren Patashnik.
Concrete mathematics. Addison-Wesley Publishing Company, Reading, MA, 1994. MR 1397498 (97d:68003) - 6.
- A. Hatcher and U. Oertel.
Boundary slopes for Montesinos knots. Topology, 28(4):453-480, 1989. MR 1030987 (91e:57016) - 7.
- A. Hatcher and W. Thurston.
Incompressible surfaces in -bridge knot complements. Invent. Math., 79(2):225-246, 1985. MR 778125 (86g:57003) - 8.
- Jim Hoste and Morwen Thistlethwaite.
Knotscape. http://www.math.utk.edu/morwen, 1998. - 9.
- Alan E. Lash.
Boundary curve space of the Whitehead link complement. Ph.D. thesis, University of California, Santa Barbara, 1993. - 10.
- Tomotada Ohtsuki.
Ideal points and incompressible surfaces in two-bridge knot complements. J. Math. Soc. Japan, 46(1):51-87, 1994. MR 1248091 (94k:57016) - 11.
- Dale Rolfsen.
Knots and links, volume 7 of Mathematics Lecture Series. Publish or Perish Inc., Houston, TX, 1990. MR 1277811 (95c:57018)
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Additional Information:
Jim
Hoste
Affiliation:
Pitzer College, 1050 N. Mills Ave., Claremont, California 91711
Email:
jhoste@pitzer.edu
Patrick
D.
Shanahan
Affiliation:
Loyola Marymount University, 1 LMU Dr., Los Angeles, California 90045-2659
Email:
pshanahan@lmu.edu
DOI:
10.1090/S0025-5718-07-01936-9
PII:
S 0025-5718(07)01936-9
Keywords:
Knot,
link,
2-bridge,
boundary slope
Received by editor(s):
May 24, 2005
Received by editor(s) in revised form:
March 31, 2006
Posted:
March 12, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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