Surgery on a knot in (Surface x I)
Geometric Topology
2014-10-01 v2
Abstract
Suppose F is a compact orientable surface, K is a knot in F x I, and N is the 3-manifold obtained by some non-trivial surgery on K. If F x {0} compresses in N, then there is an annulus in F x I with one end K and the other end an essential simple closed curve in F x {0}. Moreover, the end of the annulus at K determines the surgery slope. An application: suppose M is a compact orientable 3-manifold that fibers over the circle. If surgery on a knot K in M yields a reducible manifold, then either: the projection of K to S^1 has non-trivial winding number; or K lies in a ball; or K lies in a fiber; or K is a cabled knot.
Keywords
Cite
@article{arxiv.0807.0405,
title = {Surgery on a knot in (Surface x I)},
author = {Martin Scharlemann and Abigail Thompson},
journal= {arXiv preprint arXiv:0807.0405},
year = {2014}
}
Comments
Revised to include reference to Yi Ni's related "Dehn surgeries that yield fibred 3-manifolds", arXiv:0712.4387