2011/02/04 by Stefan Friedl, Stefano Vidussi
Mathematics · #math.GT #math.SG #msc:53D05
published as Proc. Roy. Soc. Edinburgh Sect. A 142 (2012), no. 2, 359-370 · 11 pages
arxiv created 2011/02/04 · arxiv updated 2018/12/24
Let M be a closed 4-manifold with a free circle action. If the orbit manifold N3 satisfies an appropriate fibering condition, then we show how to represent a cone in H2(M;\R) by symplectic forms. This generalizes earlier constructions by Thurston, Bouyakoub and Fernández-Gray-Morgan. In the case that M is the product 4-manifold S1× N our construction complements the results of \citeFV08 (arXiv:0805:1234 [math.GT]) and allows us to completely determine the symplectic cone of such 4-manifolds. The content of this paper partly overlaps with the content of the unpublished preprint "Symplectic 4-manifolds with a free circle action" (arXiv:0801.1313 [math.GT]).