Left-orderable, non-L-space surgeries on knots

Abstract

Let K be a knot in the 3--sphere. An r-surgery on K is left-orderable if the resulting 3--manifold K(r) of the surgery has left-orderable fundamental group, and an r-surgery on K is called an L-space surgery if K(r) is an L-space. A conjecture of Boyer, Gordon and Watson says that non-reducing surgeries on K can be classified into left-orderable surgeries or L-space surgeries. We introduce a way to provide knots with left-orderable, non-L-space surgeries. As an application we present infinitely many hyperbolic knots on each of which every nontrivial surgery is a hyperbolic, left-orderable, non-L-space surgery.

23 pages, substantial revisions of the previously posted paper. To appear in Comm. Anal. Geom

References in corpus (5)

• On L-spaces and non left-orderable 3-manifold groups
• Non-left-orderable double branched coverings
• On L-spaces and left-orderable fundamental groups
• Graph manifolds Z-homology 3-spheres and taut foliations
• Left-orderable fundamental group and Dehn surgery on twist knots