Cabling, contact structures and mapping class monoids

Kenneth L. Baker, John B. Etnyre, Jeremy Van Horn-Morris

Research output: Contribution to journalArticle

21 Scopus citations

Abstract

In this paper we discuss the change in contact structures as their supporting open book decompositions have their binding components cabled. To facilitate this and applications we define the notion of a rational open book decomposition that generalizes the standard notion of open book decomposition and allows one to more easily study surgeries on transverse knots. As a corollary to our investigation we are able to show there are Stein fillable contact structures supported by open books whose monodromies cannot be written as a product of positive Dehn twists. We also exhibit several monoids in the mapping class group of a surface that have contact geometric significance.

Original languageEnglish (US)
Pages (from-to)1-80
Number of pages80
JournalJournal of Differential Geometry
Volume90
Issue number1
DOIs
StatePublished - Jan 1 2012

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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