Weighted homogeneous singularities and rational homology disk smoothings

Details Weighted homogeneous singularities and rational homology disk smoothings Weighted homogeneous singularities and rational homology disk smoothings

2009-02-13

arxiv.org/abs/0902.2277v2

Mathematics

Symplectic Geometry

45 pages, 13 figures; proofs are streamlined and unified

Scientific paper

We classify the resolution graphs of weighted homogeneous surface singularities which admit rational homology disk smoothings. The nonexistence of rational homology disk smoothings is shown by symplectic geometric methods, while the existence is verified via smoothings of negative weights. In particular, it is shown that a (negative definite) starshaped plumbing tree gives rise to a weighted homogeneous singularity admitting a rational homology disk smoothing if and only if the Milnor fillable contact structure of the link admits a weak symplectic rational homology disk filling.

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