Year: 2009
Type: article
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 f0g 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 f0g.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 !S 1 has nontrivial winding number, K lies in a ball, K lies in a fiber, or K is cabled.
Source: Algebraic & Geometric Topology
Authors: Martin Scharlemann, Abigail A Thompson
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: National Science Foundation
OpenAlex ID: W1966892391