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Journal of Topology 2008 1(2):477-517; doi:10.1112/jtopol/jtn009
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© 2008 London Mathematical Society

Rational blowdowns and smoothings of surface singularities

András I. Stipsicz

Rényi Institute of Mathematics, Hungarian Academy of Sciences H-1053 Budapest Reáltanoda utca 13–15 Hungary stipsicz@math-inst.hu

Zoltán Szabó

Department of Mathematics, Princeton University, Princeton, NJ 08544, USA szabo@math.princeton.edu

Jonathan Wahl

Department of Mathematics, The University of North Carolina, Chapel Hill, NC 27599-3250 USA jmwahl@email.unc.edu


  Abstract

In this paper, we give a necessary combinatorial condition for a negative-definite plumbing tree to be suitable for rational blowdown, or to be the graph of a complex surface singularity which admits a rational homology disk smoothing. New examples of surface singularities with rational homology disk smoothings are also presented; these include singularities with resolution graph having valency 4 nodes.

Received July 25, 2007.

2000 Mathematics Subject Classification 14J17, 32S25


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