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The Alexander polynomial of (1,1)-knots
Alessia Cattabriga
In this paper we investigate the Alexander polynomial of (1,1)-knots, which are knots lying in a 3-manifold with genus one at most, admitting a particular decomposition. More preci…
Representations of (1,1)-knots
Alessia Cattabriga, Michele Mulazzani
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 elemen…
All strongly-cyclic branched coverings of (1,1)-knots are Dunwoody manifolds
Alessia Cattabriga, Michele Mulazzani
We show that every strongly-cyclic branched covering of a (1,1)-knot is a Dunwoody manifold. This result, together with the converse statement previously obtained by Grasselli and…
(1,1)-knots via the mapping class group of the twice punctured torus
Alessia Cattabriga, Michele Mulazzani
We develop an algebraic representation for (1,1)-knots using the mapping class group of the twice punctured torus MCG(T,2). We prove that every (1,1)-knot in a lens space L(p,q) ca…
Strongly-cyclic branched coverings of (1,1)-knots and cyclic presentations of groups
Alessia Cattabriga, Michele Mulazzani
We study the connections among the mapping class group of the twice punctured torus, the cyclic branched coverings of (1,1)-knots and the cyclic presentations of groups. We give th…