On left-orderable fundamental groups and Dehn surgeries on knots

Abstract

We show that the resulting manifold by $r$-surgery on a large class of two-bridge knots has left-orderable fundamental group if the slope $r$ satisfies certain conditions. This result gives a supporting evidence to a conjecture of Boyer, Gordon and Watson that relates $L$-spaces and the left-orderability of their fundamental groups.

Very minor changes. To appear in the Journal of the Mathematical Society of Japan