Smoothings of singularities and symplectic surgery

Heesang Park, A. Stipsicz

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Suppose that C is a connected configuration of two-dimensional symplectic submanifolds in a symplectic 4-manifold with negative definite intersection graph ΓC. Let (S, 0) be a normal surface singularity with resolution graph ΓC and suppose that WS is a smoothing of (S, 0). We show that if we replace an appropriate neighborhood of C with WS, then the resulting 4-manifold admits a symplectic structure. The operation generalizes the rational blow-down operation of Fintushel-Stern, and therefore our result extends Symington's theorem about symplectic rational blow-downs.

Original languageEnglish
Pages (from-to)585-597
Number of pages13
JournalJournal of Symplectic Geometry
Volume12
Issue number3
DOIs
Publication statusPublished - 2014

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Surgery
Smoothing
4-manifold
Singularity
Normal Surface
Intersection Graphs
Symplectic Structure
Submanifolds
Generalise
Configuration
Graph in graph theory
Theorem

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Smoothings of singularities and symplectic surgery. / Park, Heesang; Stipsicz, A.

In: Journal of Symplectic Geometry, Vol. 12, No. 3, 2014, p. 585-597.

Research output: Contribution to journalArticle

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