Vol. 254, No. 1, 2011

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Milnor open books of links of some rational surface singularities

Mohan Bhupal and Burak Ozbagci

Vol. 254 (2011), No. 1, 47–65
Abstract

We determine Legendrian surgery diagrams for the canonical contact structures of links of rational surface singularities that are also small Seifert fibered 3-manifolds. Moreover, we describe an infinite family of Milnor fillable contact 3-manifolds so that, for each member of this family, the Milnor genus and Milnor norm are strictly greater than the support genus and support norm of the canonical contact structure. For some of these contact structures we construct supporting Milnor open books.

Keywords
contact structure, Milnor open book, support genus, surface singularity, Milnor fillable, Milnor genus
Mathematical Subject Classification 2010
Primary: 32S25, 32S55, 53D10, 57R17
Milestones
Received: 10 December 2010
Revised: 18 August 2011
Accepted: 31 August 2011
Published: 7 February 2012
Authors
Mohan Bhupal
Department of Mathematics
Middle East Technical University
06531 Ankara
Turkey
http://www.metu.edu.tr/~bhupal/
Burak Ozbagci
Department of Mathematics
Koç University
34450 Istanbul
Turkey
http://home.ku.edu.tr/~bozbagci/