An Algorithm to Find Ribbon Disks for Alternating Knots

References

• Aceto, P. (2020). Rational homology cobordisms of plumbed 3-manifolds. Algebraic Geom. Topol. 20: 1073–1126.
   Google Scholar
• Aceto, P., Meier, J., Miller, A. N., Miller, M., Park, J., Stipsicz, A. I. (2020). Branched covers bounding rational homology ball. Algebraic Geom. Topol. arXiv:2002.10324 (accepted).
   Google Scholar
• Akbulut, S. (2016). 4-Manifolds. Oxford Graduate Texts in Mathematics, Vol. 25. Oxford: Oxford University Press.
   Google Scholar
• Akbulut, S., Kirby, R. (1979/80). Branched covers of surfaces in 4-manifolds. Math. Ann. 252(2): 111–131.
   Google Scholar
• Baker, K. L., Buck, D., Lecuona, A. G. (2016). Some knots in S1×S2 with lens space surgeries. Commun. Anal. Geom. 24(3): 431–470.
   Google Scholar
• Kenneth L. Baker and John Luecke (2020). Asymmetric L-space knots, Geom. Topol. 24(5): 2287–2359.
   Google Scholar
• Brejevs, V. (2020). Ribbon surfaces for some alternating 3-braid closures. arXiv:2012.00577.
   Google Scholar
• Livingston, C., Moore, A. H. Table of knot invariants. http://www.indiana.edu/∼knotinfo.
   Google Scholar
• Crowell, R. (1959). Genus of alternating link types. Ann. Math. (2) 69: 258–275.
   Web of Science ®Google Scholar
• Culler, M., Dunfield, N. M., Goerner, M., Weeks, J. R. (2022). SnapPy, a computer program for studying the geometry and topology of 3-manifolds. http://snappy.computop.org.
   Google Scholar
• Donald, A., Owens, B. (2012). Concordance groups of links. Algebraic Geom. Topol. 12(4): 2069–2093.
   Google Scholar
• Donaldson, S. K. (1987). The orientation of Yang-Mills moduli spaces and 4-manifold topology. J. Differ. Geom. 26(3): 397–428.
   Web of Science ®Google Scholar
• Flint, O., Rankin, S., de Vries, P. (2003). Prime alternating knot generator. http://www-home.math.uwo.ca/∼srankin/papers/knots/pakg.html.
   Google Scholar
• Fox, R. H., Milnor, J. W. (1966). Singularities of 2-spheres in 4-space and cobordism of knots. Osaka Math. J. 3: 257–267.
   Google Scholar
• Goeritz, L. (1933). Knoten und quadratische Formen. Math. Z. 36(1): 647–654.
   Google Scholar
• Gordon, C. McA., Litherland, R. A. (1978). On the signature of a link. Invent. Math. 47(1): 53–69.
   Web of Science ®Google Scholar
• Greene, J. E. (2017). Alternating links and definite surfaces. Duke Math. J. 166(11): 2133–2151, with an appendix by András Juhász and Marc Lackenby.
   Google Scholar
• Herald, C., Kirk, P., Livingston, C. (2010). Metabelian representations, twisted Alexander polynomials, knot slicing, and mutation. Math. Z. 265(4): 925–949.
   Web of Science ®Google Scholar
• Howie, J. A. (2017). A characterisation of alternating knot exteriors. Geom. Topol. 21(4): 2353–2371.
   Google Scholar
• Lisca, P. (2007). Lens spaces, rational balls and the ribbon conjecture. Geom. Topol. 11: 429–472.
   Google Scholar
• Lisca, P. (2007). Sums of lens spaces bounding rational balls. Algebraic Geom. Topol. 7: 2141–2164.
   Google Scholar
• McCoy, D. (2017). Alternating knots with unknotting number one. Adv. Math. 305: 757–802.
   Web of Science ®Google Scholar
• Menasco, W. (1984). Closed incompressible surfaces in alternating knot and link complements. Topology 23(1): 37–44.
   Google Scholar
• Murasugi, K. (1958). On the genus of the alternating knot. I, II. J. Math. Soc. Japan 10: 94–105, 235–248.
   Google Scholar
• Owens, B. (2018). Equivariant embeddings of rational homology balls. Q. J. Math. 69(3): 1101–1121.
   Google Scholar
• Plesken, W. (1995). Solving XXtr=A over the integers. Linear Algebra Appl. 226/228: 331–344.
   Google Scholar
• Rasmussen, J. (2010). Khovanov homology and the slice genus. Invent. Math. 182(2): 419–447.
   Web of Science ®Google Scholar
• Rolfsen, D. (1990). Knots and Links. Mathematics Lecture Series, Vol. 7. Houston, TX: Publish or Perish, Inc. Corrected reprint of the 1976 original.
   Google Scholar
• Sartori, A. (2010). Knot concordance in three manifolds. Masters thesis. University of Pisa.
   Google Scholar
• Seeliger, A. (2014). Symmetrische Vereinigungen als Darstellungen von Bandknoten bis 14 Kreuzungen (Symmetric union presentations for ribbon knots up to 14 crossings). Diploma thesis. Stuttgart University.
   Google Scholar
• Swenton, F. Knot-like objects (KLO) software. http://KLO-Software.net.
   Google Scholar
• Tait, P. G. (1877). On knots, I. Trans. R. Soc. Edinb. 28: 145–190.
   Google Scholar
• The Sage Developers. (2021). Sagemath, the Sage Mathematics Software System (Version 9.3). https://www.sagemath.org.
   Google Scholar
• Tsukamoto, T. (2004). A criterion for almost alternating links to be non-splittable. Math. Proc. Cambridge Philos. Soc. 137(1): 109–133.
   Google Scholar
• Tsukamoto, T. (2009). The almost alternating diagrams of the trivial knot. J. Topol. 2(1): 77–104.
   Google Scholar
• Turaev, V. G. (1988). Classification of Oriented Montesinos Links via Spin Structures. Topology and Geometry—Rohlin Seminar, Lecture Notes in Mathematics, Vol. 1346. Berlin: Springer, pp. 271–289.
   Google Scholar
• Weeks, J. Snappea. http://www.geometrygames.org/SnapPea/.
   Google Scholar