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Original Articles

A Counterexample to the Bernhard–Jablan Unknotting Conjecture

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References

  • [Bernhard 94] J. Bernhard. “Unknotting Numbers and Minimal Knot Diagrams.” J. Knot Theory Ramifications 3 (1994), 1–5.
  • [Bleiler 84] S. Bleiler. “A Note on Unknotting Number.” Math. Proc. Cambridge Philos. Soc. 96 (1984), 469–471.
  • [Borodzik and Friedl 15] M. Borodzik and S. Friedl. “The Unknotting Number and Classical Invariants I.” Algebr. Geom. Topol. 15 (2015), 85–135.
  • [Cha and Livingston 17] J. Cha and C. Livingston. “KnotInfo: Table of Knot Invariants.” (http://www.indiana.edu/knotinfo), 2017.
  • [Cochran and Lickorish 86] T. Cochran and W.B.R. Lickorish. “Unknotting Information from 4-Manifolds.” Trans. Amer. Math. Soc. 297 (1986), 125–142.
  • [Culler et al.] M. Culler, N. Dunfield, M. Goerner, and J. Weeks. “SnapPy, A Computer Program for Studying the Geometry and Topology of 3-Manifolds.” (http://snappy.computop.org).
  • [Gordon and Luecke 89] C. McA. Gordon and J. Luecke. “Knots are Determined by Their Complements.” J. Amer. Math. Soc. 2 (1989), 371–415.
  • [Hoste and Thistlethwaite] J. Hoste and M. Thistlethwaite. “Knotscape.” (http://www.math.utk.edu/∼morwen/knotscape.html).
  • [Jablan 98] S. Jablan. “Unknotting Number and ∞-Unknotting Number of a Knot.” Filomat. 12 (1998), 113–120.
  • [Jablan and Sazdanović 07] S. Jablan and R. Sazdanović. “Unlinking Number and Unlinking Gap.” J. Knot Theory Ramifications 16 (2007), 1331–1355.
  • [Kanenobu and Murakami 86] T. Kanenobu and H. Murakami. “Two-Bridge Knots with Unknotting Number One.” Proc. Amer. Math. Soc. 98 (1986), 499–502.
  • [Kauffman 87] L. Kauffman, “State Models and the Jones Polynomial.” Topology. 26 (1987), 395–407.
  • [Kawamura 98] T. Kawamura. “The Unknotting Numbers of 10139 and 10152 are 4.” Osaka J. Math. 35 (1998), 539–546.
  • [Kronheimer and Mrowka 93] P. Kronheimer and T. Mrowka. “Gauge Theory for Embedded Surfaces. I.” Topology. 32 (1993),773–826.
  • [Lewark and McCoy 17] L. Lewark and D. McCoy. “On Calculating the Slice Genera of 11- and 12-Crossing Knots.” Exp. Math. (2017), 1–14. doi:https://doi.org/10.1080/10586458.2017.1353453.
  • [Lickorish 85] W.B.R. Lickorish. “The Unknotting Number of a Classical Knot, in Combinatorial Methods in Topology and Algebraic Geometry.” Contemp. Math. 44 (1985), 117–121.
  • [Livingston 02] C. Livingston. “The Slicing Number of a Knot.” Algebr. Geom. Topol. 2 (2002), 1051–1060.
  • [McCoy 17] D. McCoy. “Alternating Knots with Unknotting Number One.” Adv. Math. 305 (2017), 757–802.
  • [Menasco and Thistlethwaite 93] W. Menasco and M. Thistlethwaite. “The Classification of Alternating Links.” Ann. Math. 138 (1993), 113–171.
  • [Murasugi 65] K. Murasugi. “On a Certain Numerical Invariant of Link Types.” Trans. Amer. Math. Soc. 117 (1965), 387–422.
  • [Murasugi 87] K. Murasugi. “Jones Polynomials and Classical Conjectures in Knot Theory.” Topology. 26 (1987), 87–194.
  • [Nakanishi 83] Y. Nakanishi. “Unknotting Numbers and Knot Diagrams with the Minimum Crossings.” Math. Sem. Notes Kobe Univ. 11 (1983), 257–258.
  • [Owens 08] B. Owens. “Unknotting Information from Heegaard Floer homology” Adv. Math. 217 (2008), 2353–2376.
  • [Owens 10] B. Owens. “On Slicing Invariants of Knots.” Trans. Amer. Math. Soc. 362 (2010), 3095–3106.
  • [Ozsváth and Szabó 05] P. Ozsváth and Z. Szabó. “Knots with Unknotting Number One and Heegaard Floer Homology” Topology. 44 (2005), 705–745.
  • [Rudolph 93] L. Rudolph. “Quasipositivity as an Obstruction to Sliceness.” Bull. Amer. Math. Soc. 29 (1993), 51–59.
  • [Stoimenow 04] A. Stoimenow. “Polynomial Values, the Linking Form and Unknotting Numbers.” Math. Res. Lett. 11 (2004), 755–769.
  • [Thistlethwaite 87] M. Thistlethwaite. “A Spanning Tree Expansion of the Jones Polynomial.” Topology. 26 (1987), 297–309.
  • [Zeković et al. 16] A. Zeković, S. Jablan, L. Kauffman, R. Sazdanovic and M. Stošić. “Unknotting and Maximum Unknotting Numbers.” J. Knot Theory Ramifications 25 (2016), 1641010.

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