Journal of Topology

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

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.

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2000 Mathematics Subject Classification 14J17, 32S25

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This Article Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to My Personal Archive Download to citation manager Request Permissions Google Scholar Articles by Stipsicz, A. I. Articles by Wahl, J. Social Bookmarking          What's this?