https://uiowa-applied-topology.github.io/interests/tanglenomicon/theory/ Recent content in The Tanglenomicon Theory on UIAT Hugo -- gohugo.io en © 2026 UIAT https://uiowa-applied-topology.github.io/interests/tanglenomicon/theory/arborescent/ Mon, 01 Jan 0001 00:00:00 +0000 https://uiowa-applied-topology.github.io/interests/tanglenomicon/theory/arborescent/ <p>Our arborescent tangle tabulation project presents a comprehensive study on the tabulation of arborescent tangles[<a class="hugo-simplecite-cite-hyperlink" href="#bibreference-1" title="F. Bonahon and L. Siebenmann, New Geometric Splittings of Classical Knots and the Classification and Symmetries of Arborescent Knots, https://dornsife.usc.edu/francis-bonahon/wp-content/uploads/sites/205/2023/06/BonSieb-compressed.pdf, 2016. ">1</a>]. Arborescent tangles are constructed by taking a collection of twisted bands described by a weighted tree and connecting them with successive plumbing. The arborescent tangles are shown to be equivalent to Conway&rsquo;s algebraic tangles[<a class="hugo-simplecite-cite-hyperlink" href="#bibreference-2" title="J. Conway, An enumeration of knots and links, and some of their algebraic properties, in Computational Problems in Abstract Algebra, Elsevier, 1970, pp. 329–358.doi:10.1016/B978-0-08-012975-4.50034-5">2</a>].</p>