Constrained knots in lens spaces
Abstract
In this paper, we study a special family of (1,1) knots called constrained knots, which includes 2-bridge knots in the 3-sphere S3 and simple knots in lens spaces. Constrained knots are parameterized by five integers and characterized by the distribution of spinc structures in the corresponding (1,1) diagrams. The knot Floer homology HFK of a constrained knot is thin. We obtain a complete classification of constrained knots based on the calculation of HFK and presentations of knot groups. We provide many examples of constrained knots constructed from surgeries on links in S3, which are related to 2-bridge knots and 1-bridge braids. We also show many examples of constrained knots whose knot complements are orientable hyperbolic 1-cusped manifolds with simple ideal triangulations.