Vol. 257, No. 1, 2012

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Maps on 3-manifolds given by surgery

Boldizsár Kalmár and András I. Stipsicz

Vol. 257 (2012), No. 1, 9–35
Abstract

Suppose that the 3-manifold M is given by integral surgery along a link L S3. In the following we construct a stable map from M to the plane, whose singular set is canonically oriented. We obtain upper bounds for the minimal numbers of crossing singularities, nonsimple singularities, and connected components of fibers of stable maps from M to the plane in terms of properties of L.

Keywords
stable map, 3-manifold, surgery, negative knot, Thurston-Bennequin number
Mathematical Subject Classification 2010
Primary: 57R45
Secondary: 57M27
Milestones
Received: 30 April 2011
Revised: 7 May 2012
Accepted: 9 May 2012
Published: 19 June 2012
Authors
Boldizsár Kalmár
Alfréd Rényi Institute of Mathematics
Hungarian Academy of Sciences
Reáltanoda utca 13-15
1053 Budapest
Hungary
András I. Stipsicz
Alfréd Rényi Institute of Mathematics
Hungarian Academy of Sciences
Reáltanoda utca 13-15
1053 Budapest
Hungary
Institute for Advanced Study
Princeton, NJ 08540
United States