On representations of 2-bridge knot groups in quaternion algebras II: The case of the Trefoil knot group

Abstract

The complete classification of representations of the Trefoil knot group G in S3 and SL(2, ℝ), their affine deformations, and some geometric interpretations of the results, are given. Among other results, we also obtain the classification up to conjugacy of the noncyclic groups of affine Euclidean isometries generated by two isometries μ and ν such that μ2 = ν3 = 1, in particular those which are crystallographic. We also prove that there are no affine crystallographic groups in the three-dimensional Minkowski space which are quotients of G.