References
- Agol, I. (2012). Unknots. https://web.archive.org/web/20120719023259/http://homepages.math.uic.edu/˜agol/unknots.html.
- Burton, B. A., Budney, R., Pettersson, W. (1999–2021). Regina: Software for low-dimensional topology. http://regina-normal.github.io/.
- Culler, M., Dunfield, N. M., Goerner, M., Weeks, J. R. (2022). SnapPy, a computer program for studying the geometry and topology of 3-manifolds. Available at http://snappy.computop.org.
- Curtis, F. (2001). Unknot equivalence. http://f2.org/maths/kt/unknoteq.html.
- Dynnikov, I. A. (2006). Arc-presentations of links: Monotonic simplification. Fund. Math. 190: 29–76. 10.4064/fm190-0-3
- Freedman, M. H., He, Z.-H., Wang, Z. (1994). Mobius energy of knots and unknots. Ann. Math. 139(1): 1–50.
- Goeritz, L. (1934). Bemerkungen zur knotentheorie. Abh. Math. Sem. Univ. Hamburg 10(1): 201–210. 10.1007/BF02940674
- Gowers, T. (2011). Are there any very hard unknots? https://mathoverflow.net/questions/53471/are-there-any-very-hard-unknots.
- Hass, J., Lagarias, J. C. (2001). The number of Reidemeister moves needed for unknotting. J. Amer. Math. Soc. 14(2): 399–428.
- Hass, J., Nowik, T. (2008). Invariants of knot diagrams. Math. Ann. 342(1): 125–137.
- Hass, J., Nowik, T. (2010). Unknot diagrams requiring a quadratic number of Reidemeister moves to untangle. Discrete Comput. Geom. 44(1): 91–95.
- Hass, J., Snoeyink, J., Thurston, W. P. (2003). The size of spanning disks for polygonal curves. Discrete and Computational Geometry 29(1): 1–18. 10.1007/s00454-002-2707-6
- Henrich, A., Kauffman, L. H. (2014). Unknotting unknots. Amer. Math. Monthly 121(5): 379–390.
- Kauffman, L. H., Lambropoulou, S. (2012). Hard unknots and collapsing tangles. In: Kauffman, L. H., Lambropoulou, S., Jablan, S., Przytycki, J. H., eds. Introductory Lectures on Knot Theory. Series on Knots and Everything, Vol. 46. Singapore: World Scientific, pp. 187–247.
- Lackenby, M. (2015). A polynomial upper bound on Reidemeister moves. Ann. Math. 182: 491–564. 10.4007/annals.2015.182.2.3
- Moskovich, D. (2013). What is the state of the art for algorithmic knot simplification? https://mathoverflow.net/questions/144158/what-is-the-state-of-the-art-for-algorithmic-knot-simplification.
- Ochiai, M. (1990). Nontrivial projections of the trivial knot. Astérisque, 7–10. Algorithmique, topologie et géométrie algébriques (Seville, 1987 and Toulouse, 1988).
- Petronio, C., Zanellati, A. (2016). Algorithmic simplification of knot diagrams: New moves and experiments. Journal of Knot Theory and Its Ramifications 25(10): 1–30. 10.1142/S0218216516500590
- Reidemeister, R. (1927). Elementare Begründung der Knotentheorie. Abh. Math. Sem. Univ. Hamburg 5(1): 24–32. 10.1007/BF02952507
- Thiffeault, J.-L., Finn, M. D. (2006). Topology, braids and mixing in fluids. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364(1849): 3251–3266.
- Tuzun, R. E., Sikora, A. S. (2018). Verification of the Jones unknot conjecture up to 22 crossings. J. Knot Theory Ramifications 27(3): 1840009.