Outermost forks and a theorem of Jaco. (English) Zbl 0589.57011

Scharlemann, Martin

Combinatorial methods in topology and algebraic geometry, Proc. Conf. Hon. A. M. Stone, Rochester/N. Y. 1982, Contemp. Math. 44, 189-193 (1985).

[For the entire collection see Zbl 0564.00013.]
The author gives another proof of a theorem due to Jaco: Let M be a compact orientable 3-manifold. If the boundary of M is compressible, but contains a simple closed curve J whose complement is incompressible, then adding a 2-handle along J produces a 3-manifold with incompressible boundary. The proof adds nothing really new, but does provide a clear exposition of the use of the technique of ”outermost forks” for analyzing intersections of disks and surfaces.

Reviewer: N.Smythe

MSC:

57N10	Topology of general \(3\)-manifolds (MSC2010)
57R65	Surgery and handlebodies

Keywords:

compact orientable 3-manifold; boundary; compressible; simple closed curve; 2-handle; incompressible boundary

Citations:

Zbl 0564.00013