On Calculating the Slice Genera of 11- and 12-Crossing Knots

References

• [Baader et al. 15] S. Baader, P. Feller, L. Lewark, and L. Liechti. “On the Topological 4-genus of Torus Knots.” Accepted for publication by Trans. Amer. Math. Soc. arXiv:1509.07634, 2015.
   Google Scholar
• [Baader and Lewark 15] S. Baader and L. Lewark. “The Stable 4-genus of Alternating Knots.” Accepted for publication by Asian J. Math. arXiv:1505.03345, 2015.
   Google Scholar
• [Casson and Gordon 86] A. J. Casson and C. McA. Gordon. “Cobordism of Classical Knots.” In À la recherche de la topologie perdue, volume 62 of Progr. Math., pp. 181–199. Boston, MA: Birkhäuser Boston, 1986. With an appendix by P. M. Gilmer.
   Google Scholar
• [Cha 08] J. C. Cha. “Topological Minimal Genus and L2-Signatures.” Algebr. Geom. Topol. 8:2 (2008), 885–909.
   Web of Science ®Google Scholar
• [Cha and Livingston 16] J. C. Cha and C. Livingston. “Knotinfo: Table of Knot Invariants.” http://www.indiana.edu/∼knotinfo/, 2016.
   Google Scholar
• [Donaldson 87] S. K. Donaldson. “The Orientation of Yang-Mills Moduli Spaces and 4-manifold Topology.” J. Diff. Geom. 26:3 (1987), 397–428.
   Web of Science ®Google Scholar
• [Feller 16] P. Feller. “The Degree of the Alexander Polynomial is an Upper Bound for the Topological Slice Genus.” Geom. Topol. 20:3 (2016), 1763–1771.
   Web of Science ®Google Scholar
• [Feller and Lewark 16] P. Feller and L. Lewark. “On Classical Upper Bounds for Slice Genera.” arXiv:1611.02679, 2016.
   Google Scholar
• [Feller and McCoy 16] P. Feller and D. McCoy. “On 2-bridge Knots with Differing Smooth and Topological Slice Genera.” Proc. Amer. Math. Soc. 144:12 (2016), 5435–5442.
   Web of Science ®Google Scholar
• [Freedman 82] M. H. Freedman. “The Topology of Four-dimensional Manifolds.” J. Diff. Geom. 17:3 (1982), 357–453.
   Web of Science ®Google Scholar
• [Freedman and Quinn 90] M. H. Freedman and F. Quinn. Topology of 4-manifolds, volume 39 of Princeton Mathematical Series. Princeton, NJ: Princeton University Press, 1990.
   Google Scholar
• [Gompf and Stipsicz 99] R. Gompf and A. Stipsicz. 4-manifolds and Kirby calculus, Volume 20 of Graduate Studies in Mathematics. Providence, RI: American Mathematical Society, 1999.
   Google Scholar
• [Gordon and Litherland 78] C. McA. Gordon and R. A. Litherland. “On the Signature of a Link.” Invent. Math. 47:1 (1978), 53–69.
   Web of Science ®Google Scholar
• [Herald et al. 10] C. Herald, P. Kirk, and C. Livingston. “Metabelian Representations, Twisted Alexander Polynomials, Knot Slicing, and Mutation.” Math. Z. 265:4 (2010), 925–949.
   Web of Science ®Google Scholar
• [Hoste and Thistlethwaite 99] J. Hoste and M. Thistlethwaite. Knotscape (version 1.01), 1999. Computer program.
   Google Scholar
• [Kauffman and Taylor 76] L. H. Kauffman and L. R. Taylor. “Signature of Links.” Trans. Amer. Math. Soc. 216 (1976), 351–365.
   Web of Science ®Google Scholar
• [Kirby and Siebenmann 77] R. C. Kirby and L. C. Siebenmann. Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1977. With notes by John Milnor and Michael Atiyah, Annals of Mathematics Studies, No. 88.
   Google Scholar
• [Koprowski and Czogała 13] P. Koprowski and A. Czogała. “Computing with Quadratic Forms Over Number Fields.” arXiv:1304.0708, 2013.
   Google Scholar
• [Kronheimer and Mrowka 93] P. B. Kronheimer and T. S. Mrowka. “Gauge Theory for Embedded Surfaces I.” Topology 32:4 (1993), 773–826.
   Google Scholar
• [Lam 05] T. Y. Lam. Introduction to Quadratic Forms Over Fields, volume 67 of Graduate Studies in Mathematics. Providence, RI: American Mathematical Society, 2005.
   Google Scholar
• [Levine 69] J. Levine. “Invariants of Knot Cobordism.” Invent. Math. 8:2 (1969), 98–110.
   Web of Science ®Google Scholar
• [Murakami 90] H. Murakami. “Algebraic Unknotting Operation.” In Proceedings of the Second Soviet-Japan Joint Symposium of Topology (Khabarovsk, 1989), volume 8 of Questions Answers Gen. Topology, pp. 283–292, 1990.
   Google Scholar
• [Ozsváth and Szabó 04] P. Ozsváth and Z. Szabó. “Holomorphic Disks and Genus Bounds.” Geom. Topol. 8 (2004), 311–334.
   Web of Science ®Google Scholar
• [Lickorish 97] W. B. R. Lickorish. An Introduction to Knot Theory, volume 175 of Graduate Texts in Mathematics. New York: Springer-Verlag, 1997.
   Google Scholar
• [Ranicki 98] A. Ranicki. High-dimensional Knot Theory. Springer Monographs in Mathematics. New York: Springer-Verlag, 1998. Algebraic surgery in codimension 2, With an appendix by Elmar Winkelnkemper.
   Google Scholar
• [Rasmussen 10] J. Rasmussen. “Khovanov Homology and the Slice Genus.” Invent. Math. 182:2 (2010), 419–447.
   Web of Science ®Google Scholar
• [The PARI Group, Bordeaux 15] The PARI Group, Bordeaux. PARI/GP, version 2.7.4, 2015. Programming library available from http://pari.math.u-bordeaux.fr/.
   Google Scholar
• [The GAP Group 15] The GAP Group. GAP – Groups, Algorithms, and Programming, Version 4.7.8, 2015.
   Google Scholar
• [Taylor 79] L. R. Taylor. “On the Genera of Knots.” In Topology of low-dimensional manifolds (Proc. Second Sussex Conf., Chelwood Gate, 1977), volume 722 of Lecture Notes in Math., pp. 144–154. Berlin: Springer, 1979.
   Google Scholar
• [Tristram 69] A. G. Tristram. “Some Cobordism Invariants for Links.” Proc. Cambridge Philos. Soc. 66:2 (1969), 251–264.
   Google Scholar