Publications

Papers that have been submitted for publication:


Papers that have been accepted for publication:


  1. Signatures of real algebraic curves via plumbing diagrams (with Stepan Yu. Orevkov), Jour. not Th. Ramif.(special issue for Conference on Knot Theory and Its Applications to Physics and Quantum Computing) arXiv:1510.06377, 28 pages

  2. On the Kauffman bracket skein module of the 3-torus. Indiana University Math. Jour, arXiv:1604.02075, 5 pages

Papers that have been published:


  1. An application of TQFT to modular representation theory (with Gregor Masbaum), Invent. Math. (2017) 210: 510-530

  2. Signature Jumps and Alexander Polynomials for Links (with Charles Livingston), Proc. AMS, 144, (2016) 5407--5417

  3. Even and odd Kauffman bracket ideals for genus-1 tangles (with Susan M. Abernathy), New York J. Math. 22 (2016) 1039-1053

  4. Integral TQFT and modular representations (with Gregor Masbaum). Oberwolfach Reports, No 30, (2015), 1713

  5. Two functions on Sp(g,R), Comptes Rendus - Mathematique 353, Issue 6, (2015), 477-481

  6. Irreducible factors of modular representations of mapping class groups arising in Integral TQFT.(with Gregor Masbaum), Quantum Topology, 5, Issue 2, 2014, 225-258

  7. Extra structure and the universal construction for the Witten-Reshetikhin-Turaev TQFT, (with Xuanye Wang) Proc. Amer. Math. Soc. 142 (2014), 2915-2920.

  8. Maslov Index, Lagrangians, Mapping Class Groups and TQFT (with Gregor Masbaum), Forum Math. 25 (2013), no. 5, 1067-1106.

  9. On surgery curves for genus one slice knots (with Charles Livingston), Pac. J. Math. Vol. 265 (2013), No. 2, 405-425

  10. On the Turaev-Viro endomorphism, and the colored Jones polynomial (with Xuanting Cai), Algebraic & Geometric Topology, 13 (2013) 375-408

  11. Dimension formulas for some modular representations of the symplectic group in the natural characteristic (with Gregor Masbaum), J. Pure Appl. Algebra 217 (2013), no. 1, 82--86.

  12. The nonorientable four-genus of knots (with Charles Livingston), J. London Math. Soc. (2) 84 (2011) 559--577

  13. Integral TQFT for a one-holed torus (with Gregor Masbaum), Pacific Journal vol 252 No 1 (2011), 93--112.

  14. Heegaard genus, cut number, weak p-congruence, and quantum invariants, J. Knot Th and Ramif., vol 18, No.10 (2009) 1359-1368

  15. Quantum invariants and free Z_{p^2}-actions on 3-manifolds (with Khaled Qazaqzeh), Acta Mat. Vietnamica 33, No 3, (2008), 279--290

  16. Remarks on Congruence of 3-manifolds, J. Knot Th and Ramif. 16, (2007), 1357 -- 1360

  17. Integral Lattices in TQFT, (with Gregor Masbaum), Annales Scientifiques de l'Ecole Normale Superieure, 40, (2007), 815--844

  18. Congruence and Quantum invariants of 3-manifolds, Algebraic & Geometric Topology, 7 (2007), 1767--1790

  19. Arf invariants of real algebraic curves, Pacific J Math., 230,(2007), 297--313

  20. On the Kauffman bracket skein module of the quaternionic manifold (with John Harris), J. Knot Theory Ramifications, 16, (2007) 103--125

  21. On the Frohman Kania-Bartoszynska ideal, Math. Proc. Camb. Phil. Soc., 141, (2006), 265-271

  22. The parity of the Maslov index and the even cobordism category, (with Khaled Qazaqzeh), Fund. Math. 188 (2005), 95-102

  23. Integrality for TQFTs, Duke Math J, 125 (2004), no. 2, 389--413

  24. Integral bases for TQFT modules and unimodular representations of mapping class groups. (with Gregor Masbaum, Paul van Wamelen), Comment. Math. Helv. 79 (2004), no. 2, 260--284

  25. On the slice genus of links, (with Vincent Florens), Algebraic & Geometric Topology, 3, (2003), 905-920

  26. 3-manifold invariants and periodicity of homology spheres, (with Joanna Kania-Bartoszynska, and Jozef Przytycki), Algebraic & Geometric Topology, 2, (2002), 825-842

  27. The Homflypt skein module of a connected sum of 3-manifolds (with Jianyuan Zhong) , Algebraic & Geometric Topology, 1, (2001), 605-625

  28. On the Homflypt Skein Module of S^1 x S^2,(with Jianyuan Zhong), Math. Zeit., 237 (2001), 769-814

  29. Floppy Curves with Applications to Real Algebraic Curves, in Real Algebraic Geometry and Ordered Systems, ed. C. Delzell, J. Madden, Cont. Math. 253, American Math Society (2000) 39-76

  30. Quantum Invariants of periodic three-manifolds, Proceedings of the Kirby Fest,ed. J. Hass, M. Scharlemann, Geometry and Topology Monographs, 2 (1999), 157-175

  31. On the Witten-Reshetikhin-Turaev representations of mapping class groups, Proc. of A.M.S, 127 (1999), 2483--2488

  32. Topological Quantum Field Theory And Strong Shift Equivalence, Canadian Mathematical Bulletin, 42 (1999), 190-197

  33. Skein theory and Witten-Reshetikhin-Turaev Invariants of links in lens spaces, Commun. Math. Phys., 202 (1999), 411-419

  34. A TQFT for Wormhole cobordisms over the field of rational functions, Knot Theory, Warsaw 1995 ,ed V.F.R.Jones , J.Kania-Bartoszynska , J.H.Przytycki , P.Traczyk ,V.Turaev, Banach Center Publications 42,1998, 119-127

  35. Turaev-Viro Modules of Satellite Knots , Knots 96, ed S. Suzuki, World Scientific 1997, 337-363

  36. Invariants for 1-dimensional cohomology classes arising from TQFT, Topology and its Applications ,75 (1997) 217-259

  37. Real Algebraic Curves and Link Cobordism II, in Topology of Real Algebraic Varieties and related Topics eds. V.Kharlamov, A.Khorchagin, G.Polotovskii, O.Viro Amer.Math..Soc.. Transl.-( 2) vol 173, Advances in Mathematical Sciences, (1996 ) 73-84

  38. A Method for computing the Arf invariants of Links, in Quantum Topology,eds:L.H. Kaufmann , R.A. Baadhio, World Scientific Publishing Co.(1993) 174-181

  39. Link Cobordism in Rational Homology 3-spheres, The Journal of Knot Theory And Its Ramifications 2 (1993) 285-320

  40. Signatures of Singular Branched Covers, Math. Annalen 295 (1993), 645-659

  41. Classical Knot and Link Concordance, Comment. Math. Helv. 68 (1993) 1-19

  42. Discriminants of Casson-Gordon Invariants (with Charles Livingston), Math. Proc. Camb. Phil. Soc. 112 (1992), 127-139

  43. The Casson-Gordon Invariant and Link concordance (with Charles Livingston), Topology31 (1992),475-492.

  44. Real Algebraic Curves and Link Cobordism, Pacific J. Math. 153 (1992) 31-69.

  45. An Algebraic Link Concordance Group for (p, 2p - 1) - Links in S2p+1 (with Charles Livingston), Proc. of the Edinburgh Math. Soc. 34 (1991), 455-462.

  46. Algebraic Curves in RP(1) x RP(1), Proc. A.M.S. 113 (1991), 47-52.

  47. The Duality Conjecture in Formal Knot Theory (with Richard Litherland), Osaka J. Math. 23 (1986), 229-247.

  48. Ribbon concordance and a Partial Order on S-equivalence classes, Topology and its Applications, 18 (1984), 313-324.

  49. On embedding 3-manifolds in 4-space (with Charles Livingston), Topology 22, (1983), 241-252.

  50. Slice knots in S3, Quart. J. Math. Oxford 34 (1983), 305-322.

  51. On the Slice Genus of Knots, Invent. Math. 66 (1982), 191-197.

  52. Configuration of surfaces in 4-manifolds, Trans. A.M.S. 264 (1981), 353-380.

  53. Topological proof of the G-Signature Theorem for G finite, Pacific Journal of Math. 97 (1981), 105-114.