Geometry & Topology 8 (2004) 743–777

DOI: 10.2140/gt.2004.8.743

arXiv: math.GT/0401186

Abstract

Given a smooth, closed, oriented 4–manifold X and α in H₂(X,Z) such that α·α>0, a closed 2–form ø is constructed, Poincaré dual to α, which is symplectic on the complement of a finite set of unknotted circles Z. The number of circles, counted with sign, is given by d=(c₁(s)²-3σ(X)-2χ(X))/4, where s is a certain spin^C structure naturally associated to ω.

Keywords

symplectic, 4–manifold, spin^C, almost complex, harmonic

Mathematical Subject Classification

Primary: 57R17

Secondary: 32Q60, 57M50

References

Forward citations

Publication

Received: 17 January 2004
Revised: 6 May 2004
Accepted: 16 May 2004
Published: 18 May 2004
Proposed: Yasha Eliashberg
Seconded: Leonid Polterovich, Simon Donaldson

Authors