Research Interests

My research is related to knots in the 3-dimensional sphere. I have worked with knot concordance and symmetries. My recent work includes obstructing torsion in the concordance group using Heegaard-Floer homology (with Jabuka), and Casson-Gordon invariants (with Livingston); criteria for cyclic and free periodicity of knots using the twisted Alexander polynomials (with Hillman and Livingston); computations of Ozsvath-Szabo and Rasmussen invariants of doubled knots (with Livingston); equivariant concordance (with Davis).
I completed my Ph.D. in 1994 at Indiana University with thesis advisor Charles Livingston.
The following is a list of my publications and preprints, some of which can be downloaded in pdf form.

Book in Progress

  • Introduction to Knot Concordance with C. Livingston.

    Research Publications

  • Stabilizing Four-Torsion in Classical Knot Concordance with C. Livingston, Top. Proc. 37 (2011) pp. 119-128. (E-published on May 18, 2010) arXiv preprint.

  • Order in the concordance group and Heegaard Floer homology, with S. Jabuka, Geometry and Topology, 11 (2007) 979-994.

  • Ozsvath-Szabo and Rasmussen invariants of doubled knots, with C. Livingston, Algebraic and Geometric Topology, 6 (2006) 651-657.

  • The Twisted Alexander Polynomial and Periodicity of Knots, with J. Hillman and C. Livingston, Algebraic and Geometric Topology, 6 (2006) 145-169.

  • Alexander Polynomials of Equivariant Slice Knots, with J. F. Davis, Transactions of the Amer. Math. Soc., 358 (2006), 2949-2964. arXiv preprint

  • A Move on Diagrams that Generates S-equivalence of Knots, with T. Stanford, J. Knot Theory Ramif. 12 (2003) 717-724. arXiv preprint

  • Torsion in Knot Concordance, with C. Livingston, Asian J. Math. 5 (2001) 161-168. arXiv preprint

  • Computation of Lickorish's 3-manifold Invariant using Chern-Simmons Theory, with P. Ramadevi, Commun. Math. Phy. 209 (2000) 29-49. arXiv preprint

  • Obstructing 4-torsion in the knot concordance group, with C. Livingston, J. Diff. Geom. 51 (1999) 1-12. arXiv preprint

  • Equivariant Concordance of Knots in $S^3$, Knots '96, Proceedings of the Fifth International Research Institute of Mathematical Society of Japan, held at Waseda University, Tokyo, July 1996, ed. S. Suzuki, World Scientific, 1997, 81-89. Preprint

  • New Invariants of Periodic Knots, Math. Proc. Camb. Phil. Soc. 122 (1997) 281-290.

  • Casson-Gordon Invariants of Genus 1 Knots and Concordance to Reverses, J. Knot Theory Ramif. 5 (1996) 661-677.

  • Periodicity, Genera and Alexander Polynomials of Knots, Pacific J. Math. 166 (1994) 357-371.

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    last updated on Sun Oct 9 14:23:56 PDT 2011