Positive open book decompositions of Stein fillable 3-manifolds along prescribed links

Research output: Contribution to journalArticle

Abstract

It is known by Loi and Piergallini that a closed, oriented, smooth 3-manifold is Stein fillable if and only if it has a positive open book decomposition. In the present paper we will show that for every link L in a Stein fillable 3-manifold there exists an additional knot L′ to L such that the link L ∪ L′ is the binding of a positive open book decomposition of the Stein fillable 3-manifold. To prove the assertion, we will use the divide, which is a generalization of real morsification theory of complex plane curve singularities, and 2-handle attachings along Legendrian curves.

Original languageEnglish
Pages (from-to)325-342
Number of pages18
JournalTopology
Volume45
Issue number2
DOIs
Publication statusPublished - 2006 Mar 1
Externally publishedYes

Fingerprint

Open Book Decomposition
Plane Curve
Assertion
Argand diagram
Knot
Divides
Singularity
If and only if
Closed
Curve

Keywords

  • Divide
  • Lefschetz fibration
  • Positive open book decomposition
  • Stein fillable 3-manifold

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Positive open book decompositions of Stein fillable 3-manifolds along prescribed links. / Ishikawa, Masaharu.

In: Topology, Vol. 45, No. 2, 01.03.2006, p. 325-342.

Research output: Contribution to journalArticle

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