TY - JOUR

T1 - Holomorphic triangle invariants and the topology of symplectic four-manifolds

AU - Ozsváth, Peter

AU - Szabó, Zoltán

PY - 2004/1/1

Y1 - 2004/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=1642587273&partnerID=8YFLogxK

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U2 - 10.1215/S0012-7094-04-12111-6

DO - 10.1215/S0012-7094-04-12111-6

M3 - Article

AN - SCOPUS:1642587273

VL - 121

SP - 1

EP - 34

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

SN - 0012-7094

IS - 1

ER -