Tangent circle bundles admit positive open book decompositions along arbitrary links

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3 Citations (Scopus)

Abstract

In the present paper we generalize the divide lying in the unit disk, introduced by A'Campo, to compact, oriented, smooth surfaces, and prove a fibration theorem for generalized divides. As a consequence, we will show that, for any link L in the tangent circle bundle Y to the compact surface, there exists an additional knot K such that the link L∪K is the binding of a "positive" open book decomposition of Y.

Original languageEnglish
Pages (from-to)215-232
Number of pages18
JournalTopology
Volume43
Issue number1
DOIs
Publication statusPublished - 2004 Jan 1
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

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