Volume 8, issue 2 (2004)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Constructing symplectic forms on 4–manifolds which vanish on circles

David T Gay and Robion Kirby

Geometry & Topology 8 (2004) 743–777

arXiv: math.GT/0401186

Abstract

Given a smooth, closed, oriented 4–manifold X and α H2(X, ) such that α α > 0, a closed 2–form 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 structure naturally associated to ω.

Keywords
symplectic, $4$–manifold, $\mathrm{spin}^C$, almost complex, harmonic
Mathematical Subject Classification 2000
Primary: 57R17
Secondary: 57M50, 32Q60
References
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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
David T Gay
CIRGET
Université du Québec à Montréal
Case Postale 8888
Succursale centre-ville
Montréal
Quebec H3C 3P8
Canada
Robion Kirby
Department of Mathematics
University of California
Berkeley
California 94720
USA