Research Papers

51. with Yi Ni, Characterizing slopes for torus knots, II, preprint. (pdf file)

50. with Steven Boyer and Cameron Gordon, Dehn fillings of knot manifolds containing essential twice punctured tori, to appear in Memoirs of the Amer. Math. Soc. (pdf file) (data file 1) (data file 2)

49. Remarks on SU(2)-simple knots and SU(2)-cyclic 3-manifolds, Contemp. Math. 760 (2020) 345-353.

48. with Yi Ni, Dehn surgery on knots in S^3 producing Nil Seifert fibred spaces, Ann. of Math. Studies 205 (2020) 244-258.

47. with Chris Herald, A note on orderability and Dehn filling, Proc. Amer. Math. Soc. 147 (2019) 2815-2819.

46. with Yi Ni, Finite Dehn surgeries on knots in S^3, Algebraic & Geometric Topology 18 (2018) 441-492.

45. with Thang Le, Character varieties, A-polynomials, and the AJ-conjecture, Algebraic & Geometric Topology 17 (2017) 157-188.

44. with Yi Ni, Detection of knots and a cabling formula for A-polynomials, Algebraic & Geometric Topology 17 (2017) 65-109.

43. with Dennis Ruppe, The AJ-conjecture and cabled knots over torus knots, J. Knot Theory and its Ramifications 24 (2015) 24 pages

42. with Yi Ni, Characterizing slopes for torus knots, Algebraic & Geometric Topology, 14 (2014) 1249-1274.

41. with Steven Boyer and Cameron Gordon, Dehn fillings of knot manifolds containing essential once-punctured tori, Trans. Amer. Math. Soc., 366 (2014) 341-393.

40. with Steven Boyer and Cameron Gordon, Characteristic submanifold theory and toroidal Dehn filling, Advances in Mathematics, 230 (2012) 1673-1737.

39. with Joseph Masters, Quasi-Fuchsian surfaces in hyperbolic link complements, unpublished paper.

38. with Steven Boyer and Cameron Gordon, Reducible and finite Dehn fillings, J. Lond. Math. Soc. 79 (2009) 72--84.

37. with Ian Agol and Steven Boyer, Virtually fibred Montesinos links, Journal of Topology 1 (2008) 993--1018.

36. with Joseph Masters, Closed quasi-Fuchsian surfaces in hyperbolic knot complements, Geometry & Topology 12 (2008) 2095-2171.

35. with Joseph Masters and William Menasco, Heegaard splittings and virtually Haken Dehn filling II, New York J. Math. 15 (2009) 1--17.

34. with Steven Boyer, Marc Culler and Peter Shalen, Characteristic subsurfaces, character varieties and Dehn fillings, Geometry & Topology 12 (2008) 233-297.

33. A-polynomial n-tuple of a link and hyperbolic 3-manifolds with non-integral traces, J. Knot Theory Ramifications 15 (2006) 279-287.

32. with Samuel Schack, Culler-Shalen norms and invaraint trace fields, Geometry and Topology of Manifolds, Fields Institute Communications 47 (2005) 307-311.

31. with Steven Boyer, Every nontrivial knot in the 3-sphere has nontrivial A-polynomial, Proc. Amer. Math. Soc. 133 (2005) 2813-2815.

30. Trace fields of representations and virtually Haken 3-manifolds, Q. J. Math. 56 (2005) 431-442.

29. with Srikanth Kuppum, Roots of unity associated to strongly detected boundary slopes, J. Knot Theory Ramifications 18 (2009) 1623--1636.

28. with Steven Boyer, Marc Culler and Peter Shalen, Characteristic subsurfaces and Dehn filling, Trans. Amer. Math. Soc. 357 (2005) 2389-2444.

27. with Joseph Masters and William Menasco, Heegaard splittings and virtually Haken Dehn filling, New York J. Math. 10 (2004) 133-150.

26. The C-polynomial of a knot, Topology Appl. 139 (2004) 185-198.

25. with William Menasco, Knots with braid index three have Property-P, J. Knot Theory Ramifications 12 (2003) 427-444.

24. with Steven Boyer and Erhard Luft, On the algebraic components of the SL(2, C) character varieties of knot exteriors, Topology, 41 (2002) 667-694.

23. with Steven Boyer, A proof of the finite filling conjecture, J. Diff. Geom., 59 (2001) 87-176.

22. with Steven Boyer and Cameron Gordon, Dehn fillings of large hyperbolic 3-manifolds, J. Diff. Geom., 58 (2001) 263-308.

21. with Stephen Schanuel, Detection of essential surfaces in 3-manifolds with SL_2-trees, Math. Ann., 320 (2001) 149-165.

20. with William Menasco, Notes on tangles, 2-handle additions and exceptional Dehn fillings, Pacific J. Math., 198 (2001) 149-174.

19. with Steven Boyer, On simple points of character varieties of 3-manifolds, Proceedings of Knots in Hellas 1998, World Scientific (2000) 27-35.

18. with Cameron Gordon and Ying-Qing Wu, Nonintegral toroidal Dehn surgery on hyperbolic knots in $S^3$, Proc. Amer. Math. Soc., 128 (2000), no. 6, 1869--1879.

17. with Steven Boyer, Virtual Haken 3-manifolds and Dehn filling, Topology, 39 (2000) 103-114.

16. Dehn filling with non-degenerate boundary slope rows, Topology and its Applications, 99 (1999) 99-110.

15. with Steven Boyer, A note on finite Dehn filling, Canadian Math. Bulletin, 42 (1999) 149-154.

14. with Steven Boyer, On Culler-Shalen seminorms and Dehn filling, Ann. of Math., 248 (1998) 737-801.

13. with Steven Boyer and Thomas Mattman, The fundamental polygons of twist knots and the (-2,3,7) pretzel knot, Knots' 96, World Scientific Publishing Co. Pte. Ltd. (1997) 159-172.

12. with Steven Boyer, Cyclic surgery and boundary slopes, Geometric Topology, AMS/IP Studies in Advanced Mathematics, Vol. 2 (1997) 62-79.

11. with Steven Boyer, Reducing Dehn filling and toroidal Dehn filling, Topology Appl. 68 (1996) 285-303.

10. with Steven Boyer, Finite Dehn surgery on knots, J. Amer. Math. Soc. 9 (1996) 1005-1050.

9. with Alexey Bolsinov and Anatoly Fomenko, The strong, semi-strong and quasi-semi-strong bordism groups for integrable Hamiltonian systems with two degrees of freedom, Russian J. Math. Phys. 3 (1995) 423-452.

8. with Steven Boyer, Exceptional Dehn surgery on knots, Bull. Amer. Math. Soc. 31 (1994) 197-203.

7. with Erhard Luft, Symmetric knots and the cabling conjecture, Math. Ann. 298 (1994) 489-496.

6. with Alexey Bolsinov and Anatoly Fomenko, Three types of bordisms for integrable Hamiltonian systems with two degrees of freedom, Trudy MIRAN 205 (1994) 32-72.

5. with Robion Kirby and Paul Melvin, Quantum invariants at the sixth root of unity, Commun. Math. Phys. 151 (1993) 607-617.

4. On property I for knots in $S^{3}$, Tran. Amer. Math. Soc. 339 (1993) 643-657.

3. Unknotting number one knots are prime -- a new proof, Proc. Amer. Math. Soc. (1991) 611-612.

2. Nonintegral boundary slopes exist, Fundamenta Mathematicae 138 (1991) 219-224.

1. Cyclic surgery on satellite knots, Glasgow J. Math. 3 (1991) 125-128.