Lectures on the theory of sutured 3-manifolds. (English) Zbl 0756.57007

Scharlemann, Martin G.

Algebra and topology, Proc. 5th Math. Workshop, Taejon/Korea 1990, Proc. KIT Math. Workshop 5, 25-45 (1990).

[For the entire collection see Zbl 0727.00012.]
The current topological literature contains many applications of the theory of sutured 3-manifolds. A sutured manifold \((M,\gamma)\) is a compact oriented 3-manifold \(M\) together with a partition of \(\partial M=R_ +\cup_ \gamma R_ -\) as the union of two surfaces \(R_ +\) and \(R_ -\) along their common boundary, a collection of simple closed curves \(\gamma\), called the sutures. \(R_ +\) is oriented so that its normal vector points outward and \(R_ -\) so that it points inward.
The paper is an elementary survey of the theory of 3-manifolds and the theory of sutured 3-manifolds.

Reviewer: A.K.Guts (Omsk)

MSC:

57N10	Topology of general \(3\)-manifolds (MSC2010)
57-02	Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes

Keywords:

sutured 3-manifolds

Citations:

Zbl 0727.00012