On left-orderable fundamental groups and Dehn surgeries on twist knots

Abstract

We show that the resulting manifold by $r$-surgery on the hyperbolic twist knot $K_m,m\ge 2$, has left-orderable fundamental group if the slope $r$ satisfies the condition $r\in (-4,2m)$ if $m$ is even, and $r\in [0,4]\cup (\frac{4m}{\omega }+4,2m+4)$ if $m$ is odd, where $\omega >1$ is the unique real solution of the equation $x{e}^x=4m$.

This paper has been withdrawn by the author. This paper now becomes a part of the paper arXiv:1301.2637