Cabling, contact structures and mapping class monoids

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

Research output: Contribution to journalArticle

21 Citations (Scopus)

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
StatePublished - Jan 2012

Fingerprint

Open Book Decomposition
Contact Structure
Monoids
Dehn Twist
Mapping Class Group
Surgery
Knot
Corollary
Transverse
Contact
Generalise
Class

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Geometry and Topology

Cite this

Baker, K., Etnyre, J. B., & Van Horn-Morris, J. (2012). Cabling, contact structures and mapping class monoids. Journal of Differential Geometry, 90(1), 1-80.

Cabling, contact structures and mapping class monoids. / Baker, Kenneth; Etnyre, John B.; Van Horn-Morris, Jeremy.

In: Journal of Differential Geometry, Vol. 90, No. 1, 01.2012, p. 1-80.

Research output: Contribution to journalArticle

Baker, K, Etnyre, JB & Van Horn-Morris, J 2012, 'Cabling, contact structures and mapping class monoids', Journal of Differential Geometry, vol. 90, no. 1, pp. 1-80.
Baker, Kenneth ; Etnyre, John B. ; Van Horn-Morris, Jeremy. / Cabling, contact structures and mapping class monoids. In: Journal of Differential Geometry. 2012 ; Vol. 90, No. 1. pp. 1-80.
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