Smoothings of Singularities and Symplectic Topology
We review the symplectic methods which have been applied in the classification of weighted homogeneous singularities with rational homology disk (√HD) smoothings. We also review the construction of such smoothings and show that in many cases these smoothings are unique up to symplectic deformation. In addition, we describe a method for finding differential topological descriptions (more precisely, Kirby diagrams) of the smoothings and illustrate this method by working out a family of examples.
KeywordsContact Structure Blow Down Dual Graph Intersection Multiplicity Seifert Surface
Unable to display preview. Download preview PDF.
- R. Gompf and A. Stipsicz, 4-manifolds and Kirby calculus, Graduate Studies in Mathematics 20 AMS (1999).Google Scholar
- P. Lisca, On symplectic fillings of lens spaces, Trans. Amer. Math. Soc. 360 (2008), 765-799.Google Scholar
- D. McDuff, Singularities and positivity of intersections of J-holomorphic curves, with Appendix by Gang Liu, in Holomorphic curves in Symplectic Geometry, M. Audin and F. Lafontaine, eds., Progress in Mathematics 117, Birkhauser (1994), 191–216.Google Scholar