Abstract
We present an algorithm for constructing a rectangular diagram of a Seifert surface for the link represented by an arbitrary rectangular diagram and estimate the complexity of the resulting surface diagram.
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References
Dynnikov I., “Arc-presentations of links: Monotonic simplification,” Fund. Math., vol. 190, 29–76 (2006).
Dynnikov I. A., “Transverse-Legendrian links,” Sib. Electr. Math. Reports, vol. 16, 1960–1980 (2019).
Dynnikov I. and Prasolov M., “Rectangular diagrams of surfaces: distinguishing Legendrian knots,” J. Topol., vol. 14, no. 3, 701–860 (2021).
Ozsvath P. and Szabo Z., “Holomorphic disks and topological invariants for closed three-manifolds,” Ann. Math., vol. 159, no. 3, 1027–1158 (2004).
Manolescu C., Ozsváth P., and Sarkar S., “A combinatorial description of knot Floer homology,” Ann. Math., vol. 169, no. 2, 633–660 (2009).
Dynnikov I. and Prasolov M., “Rectangular diagrams of surfaces: representability,” Mat. Sb., vol. 208, no. 6, 55–108 (2017).
Seifert H., “Über das Geschlecht von Knoten,” Math. Ann., vol. 110, no. 1, 571–592 (1935).
Acknowledgment
The author is grateful to Ivan Dynnikov for stating the problem and sagacious advise.
Funding
The author was supported by the Basis Foundation.
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Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 3, pp. 699–711. https://doi.org/10.33048/smzh.2022.63.317
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Chernavskikh, M.M. An Algorithm for Constructing the Rectangular Diagrams of a Seifert Surface. Sib Math J 63, 583–594 (2022). https://doi.org/10.1134/S003744662203017X
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DOI: https://doi.org/10.1134/S003744662203017X