Left-orderable fundamental group and Dehn surgery on twist knots
  For any hyperbolic twist knot in the 3-sphere, we show that the resulting manifold by $r$-surgery on the knot has left-orderable fundamental group if the slope $r$ satisfies the inequality $0\le r \le 4$. 
Ryoto Hakamata and Masakazu Teragaito
math.GT math.GR