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Unknotting twisted knots with Gauss diagram forbidden moves

2021/12/31 by Shudan Xue, Xue, Shudan, Qingying Deng +1
Mathematics · Medicine · #Geometric and Algebraic Topology #Botulinum Toxin and Related Neurological Disorders

paper · pdf · doi:10.48550/arxiv.2112.15263

Abstract

Twisted knot theory, introduced by M.O.Bourgoin, is a generalization of virtual knot theory. It is easily shown that any virtual knot can be deformed into a trivial knot by a finite sequence of generalized Reidemeister moves and two "forbidden moves" F1 and F2. Similarly, we show that any twisted knot also can be deformed into a trivial knot or a trivial knot with a bar by a finite sequence of extended Reidemeister moves and three "forbidden moves" T4, F1 (or F2) and F3 (or F4) .

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