# Jim Hoste Mathematical Papers

### Publications

1. Sewn-up r-link exteriors, Ph.D thesis, University of Utah, Pacific J. of Math. 112 no. 2 (1984), 347--382.
2. The Arf invariant of a totally proper link, Topology Appl. 18 (1984), 163--177.
3. The first coefficient of the Conway polynomial, Proc. Amer. Math. Soc. 95 no. 2 (1985), 299--302.
4. A new polynomial invariant of knots and links, with D. Freyd, W.B.R. Lickorish, K. Millett, A. Ocneanu, and P. Yetter, Bull. Amer. Math. Soc. 12 no. 2 (1985), 239--246.
5. A polynomial invariant of knots and links, Pacific J. Math 124 no. 2 (1986), 295--320.
6. A formula for Casson's invariant, Trans. Amer. Math. Soc. 297 no. 2 (1986), 547--562.
7. An invariant of dichromatic links, with Jozef Przytycki, Proc. Amer. Math. Soc. 105 no. 4 (1989), 1003--1007.
8. Dichromatic link invariants, with Mark Kidwell, Trans. Amer. Math. Soc. 321 no. 1 (1990), 197--229.
9. Homotopy skein modules of orientable 3-manifolds, with Jozef Przytycki, Proc. Camb. Phil. Soc. 108 (1990), 475--488.
10. Unknotting operations involving trivial tangles, with Y. Nakanishi and K. Taniyama, Osaka J. Math. 22 (1990), 555--566.
11. Minimal atlases on 3-manifolds, with F. Gonzalez-Acu\~na and J.C. Gomez-Larra\~naga, Proc. Camb. Phil. Soc. 109 (1991), 105--115.
12. A tabulation of oriented links, with Helmut Doll, Math. Comp. 57 no. 196 (1991), 747--761.
13. A survey of skein modules of 3-manifolds, with Jozef Przytycki, Knots 90 (A. Kawauchi, eds.), Proceedings of the International Conference on Knots, Osaka, Japan, 1990, Walter de Gruyter \& Co., 1992.
14. The $(2,\infty)$-skein module of lens spaces; a generalization of the Jones polynomial, with Jozef Przytycki, J. Knot Theory Ram. 2 no. 3 (1993), 321--333.
15. Tabulating alternating knots through 14 crossings, with B. Arnold, M. Au, C. Candy, K. Erdener, J. Fan, R. Flynn, R. Muir, and D. Wu, J. Knot Theory Ram. 3 no. 4 (1994), 433--437.
16. The $(2,\infty)$-skein module of Whitehead manifolds, with Jozef Przytycki, J. Knot Theory Ram. 4 no. 3 (1995),411--427.
17. The Kauffman bracket skein module of $S^1 \times S^2$, with Jozef Przytycki, Math. Z. 220 (1995), 65--73.
18. Framed link diagrams of open 3-manifolds, in Knots '96, Proceedings of the Fifth International Research Institute of Mathematical Society of Japan, Waseda Univ., Tokyo, 1996, S. Suzuki ed., World Scientific, (1997), 515--537.
19. Open 3-manifolds with infinitely many knot-surgery descriptions, in Knots '96, Proceedings of the Fifth International Research Institute of Mathematical Society of Japan, Waseda Univ., Tokyo, 1996, S. Suzuki ed., World Scientific, (1997), 539--543.
20. Tangle surgeries which preserve Jones-type polynomials, with Jozef Przytycki, Int. J. Math. 8 no. 8 (1997), 1015--1027.
21. The first 1,701,936 knots, with Morwen Thistlethwaite and Jeff Weeks, Math. Intelligencer 20, no. 4 (1998) 33--48. [pdf]
22. Trace fields of twist knots, with Patrick Shanahan, J. Knot Theory and Ramifications, 10, no. 4 (2001) 625--639.
23. A formula for the A-polynomial of twist knots, with Patrick Shanahan, J. Knot Theory and Ramifications, 13, no. 2 (2004) 193--209.
24. Commensurability classes of twist knots, with Patrick Shanahan, J. Knot Theory and Ramifications, 14, no. 1 (2005) 1--10. math.GT/0311051
25. The enumeration and classification of knots and links, Handbook of Knot Theory, W. Menasco and M. Thistlethwaite, eds., Elsevier (2005) 209--232. [pdf]
26. Remarks on Some Hyperbolic Invariants of 2-Bridge Knots, with P. Shanahan, Physical and Numerical Models in Knot Theory, Series on Knots and Everything---Vol. 36, Calvo, Millett, Rawdon, and Stasiak, eds., World Scientific Press (2005) 581--596.
27. Computing boundary slopes of 2-bridge links, with P. Shanahan, Math. Comp. 76 (2007), 1521-1545. math.GT/0505442
28. Boundary slopes of 2-bridge links determine the crossing number, with P. Shanahan, Kobe J. Math. 24 (2007) 21-39. math.GT/0603206
29. Lissajous knots and knots with Lissajous projections, with L. Zirbel, Kobe J. Math. 24 (2007) 87-106. math.GT/0605632.
30. Sampling Lissajous and Fourier knots, with A. Boocher, G. Daigle, and W. Zhang, J. Experimental Math. 18, no. 4, (2009), 481--497, arXiv:0707.4210.
31. Torus knots are Fourier-(1,1,2) knots, J. Knot Theory and Ramifications 18, No.2 (2009), 265--270, arXiv:0708.3590
32. Epimorphisms and Boundary Slopes of 2-Bridge Knots, with P. Shanahan, Algebraic and Geometric Topology 10, (2010), 1221--1244, arXiv:0708.3590.
33. Upper bounds in the Ohtsuki-Riley-Sakuma partial order on 2-bridge knots, with Scott M. Garrabrant and Patrick D. Shanahan, J. Knot Theory and Ramifications 21, No.9 (2012), arXiv:1007.3278 .
34. Twisted Alexander polynomials of 2-bridge knots, with Patrick D. Shanahan, J. Knot Theory and Ramifications 22, No.1 (2013) arXiv:1206.1894 .
35. Involutory quandles of (2,2,r)-Montesinos links, with Patrick D. Shanahan, arXiv:1602.01852.
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