Unknotting twisted knots with Gauss diagram forbidden moves

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" $F_1$ and $F_2$. 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" $T_4$, $F_1$ (or $F_2$) and $F_3$ (or $F_4$) .

arXiv comment9 pages, 14 figures