Vol. 257, No. 1, 2012

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On overtwisted, right-veering open books

Paolo Lisca

Vol. 257 (2012), No. 1, 219–225
Abstract

We exhibit infinitely many overtwisted, right-veering, non-destabilizable open books, thus providing infinitely many counterexamples to a conjecture of Honda, Kazez and Matić. The page of all our open books is a four-holed sphere and the underlying 3-manifolds are lens spaces.

Keywords
contact surgery, destabilizable diffeomorphisms, Giroux’s correspondence, open books, overtwisted contact structures, right-veering diffeomorphisms
Mathematical Subject Classification 2010
Primary: 57R17
Secondary: 53D10
Milestones
Received: 26 July 2011
Accepted: 5 December 2011
Published: 19 June 2012
Authors
Paolo Lisca
Dipartimento di Matematica “L. Tonelli”
Università di Pisa
Largo Bruno Pontecorvo, 5
56127 Pisa
Italy