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Tangles with k Ropes and 2k Hands
Version 1
: Received: 3 December 2023 / Approved: 4 December 2023 / Online: 4 December 2023 (04:16:55 CET)
How to cite: Hari, A.; Li, E.; Liu, R. Tangles with k Ropes and 2k Hands. Preprints 2023, 2023120133. https://doi.org/10.20944/preprints202312.0133.v1 Hari, A.; Li, E.; Liu, R. Tangles with k Ropes and 2k Hands. Preprints 2023, 2023120133. https://doi.org/10.20944/preprints202312.0133.v1
Abstract
This paper will explore analogs of groups formed by the transformations of two ropes as presented by Minh-Tam Quang Trinh.1 The two operations acting on these ropes are T and S, defined as twists and clockwise turns, respectively. These actions intertwine the ropes, creating tangles. T and S also have the ability to untangle the rope when used in certain combinations. In the two-rope case, these actions expressed as a group presentation were shown to be isomorphic to SL2(Z). We explored the analog of these opera- tions, T and S, and conjectured the corresponding group to which they are isomorphic. Partial proofs for this conjecture are included and future work would include proving our conjecture as well as generalizing results to k ropes.
Keywords
tangles; isomorphism; analogs of groups; matrices; group presentation
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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