Rational blowdowns and smoothings of surface singularities

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.