1. CMB Online first
|Left-orderability and Exceptional Dehn Surgery on Twist Knots|
We show that any exceptional non-trivial Dehn surgery on a twist knot, except the trefoil, yields a $3$-manifold whose fundamental group is left-orderable. This is a generalization of a result of Clay, Lidman and Watson, and also gives a new supporting evidence for a conjecture of Boyer, Gordon and Watson.
Keywords:left-ordering, twist knot, Dehn surgery
2. CMB 2006 (vol 49 pp. 624)
|On Non-Integral Dehn Surgeries Creating Non-Orientable Surfaces |
For a non-trivial knot in the $3$-sphere, only integral Dehn surgery can create a closed $3$-manifold containing a projective plane. If we restrict ourselves to hyperbolic knots, the corresponding claim for a Klein bottle is still true. In contrast to these, we show that non-integral surgery on a hyperbolic knot can create a closed non-orientable surface of any genus greater than two.
Keywords:knot, Dehn surgery, non-orientable surface