Algebraic & Geometric Topology 9 (2009) 1825–1835

DOI: 10.2140/agt.2009.9.1825

Abstract

Suppose F is a compact orientable surface, K is a knot in F × I, and (F × I)_surg is the 3–manifold obtained by some nontrivial surgery on K. If F ×{0} compresses in (F ×I)_surg, then there is an annulus in F ×I with one end K and the other end an essential simple closed curve in F ×{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 K ⊂ M yields a reducible manifold, then either

* the projection K ⊂ M → S¹ has nontrivial winding number,

* K lies in a ball,

* K lies in a fiber, or

* K is cabled.

Keywords

Dehn surgery, taut sutured manifold

Mathematical Subject Classification

Primary: 57M27

References

Publication

Received: 5 June 2009
Revised: 10 August 2009
Accepted: 11 August 2009
Published: 2 October 2009

Authors