We present two different representations of (1, 1)-knots and study some connections between them. The first representation is algebraic: every (1, 1)-knot is represented by an element of the pure mapping class group of the twice punctured torus PMCG2(T ). Moreover, there is a surjective map from the kernel of the natural homomorphism Ω : PMCG2(T ) → MCG(T ) ∼= SL(2, Z), which is a free group of...
