26 citations · 231 across the 27 of their papers we have counts for
5 papers · 1 filter
Genus one open books with non-left-orderable fundamental group
Yu Li, Liam Watson
Let be a closed, connected, orientable three-manifold admitting a genus one open book decomposition with one boundary component. We prove that if is an L-space, then the fu…
On L-spaces and left-orderable fundamental groups
Steven Boyer, Cameron McA. Gordon, Liam Watson
Examples suggest that there is a correspondence between L-spaces and 3-manifolds whose fundamental groups cannot be left-ordered. In this paper we establish the equivalence of thes…
Turaev torsion, definite 4-manifolds, and quasi-alternating knots
Joshua Evan Greene, Liam Watson
We construct an infinite family of hyperbolic, homologically thin knots that are not quasi-alternating. To establish the latter, we argue that the branched double-cover of each kno…
Graph manifolds, left-orderability and amalgamation
Adam Clay, Tye Lidman, Liam Watson
We show that every irreducible toroidal integer homology sphere graph manifold has a left-orderable fundamental group. This is established by way of a specialization of a result du…
On cabled knots, Dehn surgery, and left-orderable fundamental groups
Adam Clay, Liam Watson
Previous work of the authors establishes a criterion on the fundamental group of a knot complement that determines when Dehn surgery on the knot will have a fundamental group that…