Holomorphic triangle invariants and the topology of symplectic four-manifolds

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This article analyzes the interplay between symplectic geometry in dimension 4 and the invariants for smooth four-manifolds constructed using holomorphic triangles introduced in [20]. Specifically, we establish a nonvanishing result for the invariants of symplectic four-manifolds, which leads to new proofs of the indecomposability theorem for symplectic four-manifolds and the symplectic Thom conjecture. As a new application, we generalize the indecomposability theorem to splittings of four-manifolds along a certain class of three-manifolds obtained by plumbings of spheres. This leads to restrictions on the topology of Stein fillings of such three-manifolds.

Original languageEnglish (US)
Pages (from-to)1-34
Number of pages34
JournalDuke Mathematical Journal
Issue number1
StatePublished - 2004

All Science Journal Classification (ASJC) codes

  • General Mathematics


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