TWISTED CONJUGACY IN DIHEDRAL ARTIN GROUPS I: TORUS KNOT GROUPS

In this paper we provide an alternative solution to a result by (Juha<acute accent>sz 2011), that the twisted conjugacy problem for odd dihedral Artin groups is solvable, where an odd dihedral Artin group is a group with presentation G(m) = < a, b | m(a, b) = m(b, a)>, where m >= 3 is odd, and m(a, b) is the word abab ... of length m. Our solution provides an implementable linear time algorithm, by considering an alternative group presentation to that of a torus knot group, and working with geodesic normal forms. An application of this result is that the conjugacy problem is solvable in extensions of odd dihedral Artin groups.