Publications

Papers that have been submitted for publication:


  1. Signatures of real algebraic curves via plumbing diagrams (with Stepan Yu. Orevkov), arXiv:1510.06377, 28 pages

Papers that have been accepted for publication:


  1. An application of TQFT to modular representation theory (with Gregor Masbaum), Invent. Math. arXiv:1606.09532, 24 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. Signature Jumps and Alexander Polynomials for Links (with Charles Livingston), Proc. AMS, 144, (2016) 5407--5417

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

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

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

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

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

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

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

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

  10. 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.

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

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

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

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

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

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

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

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

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

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

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

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

  23. 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

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

  25. 3-manifold invariants and periodicity of homology spheres, (with Joanna Kania-Bartoszynska, and Jozef Przytycki), Algebraic & Geometric Topology, 2, (2002), 825-842

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

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

  28. 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

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

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

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

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

  33. 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

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

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

  36. 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

  37. 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

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

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

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

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

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

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

  44. 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.

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

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

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

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

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

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

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

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