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Original Articles

The Search for Nonsymmetric Ribbon Knots

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References

  • [Aceto 14] P. Aceto. “Symmetric Ribbon Disks.” J. Knot Theor. Ramifications 23 (2014), 1450048.
  • [Boocher et al. 09] A. Boocher, J. Daigle, J. Hoste, and W. Zheng. “Sampling Lissajous and Fourier Knots.” Exp. Math. 18 (2009), 481–497.
  • [Cha and Livingston] J. C. Cha and C. Livingston. “KnotInfo: Table of Knot Invariants.” Available online http://www.indiana.edu/∼knotinfo
  • [Cha and Livingston 18] J. C. Cha and C. Livingston. Unknown Values in the Table of Knots, preprint (last version 2018), arxiv:math.GT/0503125
  • [Eisermann 09] M. Eisermann. “The Jones Polynomial of Ribbon Links.” Geometry Topol. 13 (2009), 623–660
  • [Eisermann and Lamm 07] M. Eisermann and C. Lamm. “Equivalence of Symmetric Union Diagrams.” J. Knot Theor. Ramifications 16 (2007), 879–898
  • [Eisermann and Lamm 11] M. Eisermann and C. Lamm. “A Refined Jones Polynomial for Symmetric Unions,” Osaka J. Math. 48 (2011), 333–370.
  • [Herald et al. 10] C. Herald, P. Kirk and C. Livingston. “Metabelian Representations, Twisted Alexander Polynomials, Knot Slicing, and Mutation.” Math. Zeitschrift 265 (2010), 925–949
  • [Hoste et al. 98] J. Hoste, M. Thistlethwaite, and J. Weeks. “The First 1,701,936 Knots.” Math. Intell. 20 (1998), 33–48
  • [Kanenobu 86] T. Kanenobu. “Examples of Polynomial Invariants of Knots and Links.” Math. Ann. 275 (1986), 555–572
  • [Kanenobu 10] T. Kanenobu. “Band Surgery on Knots and Links.” J. Knot Theor. Ramifications 19 (2010), 1535–1547
  • [Kanenobu and Komatsu 17] T. Kanenobu and S. Komatsu. “Enumeration of Ribbon 2-Knots Presented by Virtual Arcs.” J. Knot Theor. Ramifications 26 (2017), 1750042
  • [Kearney 13] K. Kearney. “The Concordance Genus of 11–Crossing Knots.” J. Knot Theor. Ramifications 22 (2013), 1350077
  • [Kinoshita and Terasaka 57] S. Kinoshita and H. Terasaka. “On Unions of Knots.” Osaka Math. J. 9 (1957), 131–153.
  • [Knotscape 99] J. Hoste and M. Thistlethwaite. “Knotscape – Providing Convenient Access to Tables of Knots.” Available online http://www.math.utk.edu/∼morwen/knotscape.html, 1999
  • [Lamm 00] C. Lamm. “Symmetric Unions and Ribbon Knots.” Osaka J. Math. 37 (2000), 537–550.
  • [Lamm 06] C. Lamm. Symmetric Union Presentations for 2-Bridge Ribbon Knots, preprint (2006), arxiv:math.GT/0602395
  • [Livingston 04] C. Livingston. “The Concordance Genus of Knots.” Alg. & Geom. Topol. 4 (2004), 1–22.
  • [Piccirillo 18] L. Piccirillo: The Conway Knot is not Slice, preprint (2018), arxiv:math.GT/1808.02923
  • [Seeliger 14] A. Seeliger. “Symmetrische Vereinigungen als Darstellungen von Bandknoten bis 14 Kreuzungen (Symmetric Union Presentations for Ribbon Knots up to 14 Crossings).” Diploma thesis, Stuttgart University, 2014.
  • [Tanaka 10] T. Tanaka. “Ribbon 2-Knots With Symmetric Union Presentations.” J. Knot Theor. Ramifications 19 (2010), 1–13.
  • [Turaev 12] T. Turaev. “Knotoids.” Osaka J. Math. 49 (2012), 195–223.
  • [Watson 07] L. Watson. “Knots with Identical Khovanov Homology.” Alg. & Geom. Topol. 7 (2007), 1389–1407.
  • [Yajima 64] T. Yajima. “On Simply Knotted Spheres in R4.” Osaka J. Math. 1 (1964), 133–152.

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