2021/08/10 by Frías, José · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.2108.04404
A (1,1)-knot in the 3-sphere is a knot that admits a 1-bridge presentation with respect to a Heegaard torus in \mathbbS3. A new parameterization of (1,1)-knots distinct from the classical ones is introduced. This parameterization is obtained from minimal-length representatives of homotopy classes of arcs in the mutipunctured plane. In the particular case of satellite (1,1)-knots, it is proven that the introduced parameterization is essentially unique. A generalization of this parameterization to the family of (g,1)-knots for any g≥ 1 is proposed.