On the affine representations of the trefoil knot group

Abstract

The complete classification of representations of the Trefoil knot group G in S^{3} 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 non cyclic groups of affine Euclidean isometries generated by two isometries $\mu$ and $\nu$ such that $\mu^{2}=\nu^{3}=1$, 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.