Constructions of small symplectic 4-manifolds using luttinger surgery

Scott Baldridge Louisiana State University Paul Kirk Indiana University

Differential Geometry mathscidoc:1609.10119

Journal of Differential Geometry, 82, (2), 317-361, 2009
Luttinger surgery is used to produce minimal symplectic 4- manifolds with small Euler characteristics. We construct a minimal symplectic 4-manifold which is homeomorphic but not diffeomorphic to CP2#3CP 2 , and which contains a genus two symplectic surface with trivial normal bundle and simply-connected complement. We also construct a minimal symplectic 4-manifold which is homeomorphic but not diffeomorphic to 3CP2#5CP 2 , and which contains two disjoint essential Lagrangian tori such that the complement of the union of the tori is simply-connected. These examples are used to construct minimal symplectic manifolds with Euler characteristic 6 and fundamental group Z, Z3, or Z/p ⊕ Z/q ⊕ Z/r for integers p, q, r. Given a group G presented with g generators and r relations, a symplectic 4-manifold with fundamental group G and Euler characteristic 10 + 6(g + r) is constructed.
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@inproceedings{scott2009constructions,
  title={CONSTRUCTIONS OF SMALL SYMPLECTIC 4-MANIFOLDS USING LUTTINGER SURGERY},
  author={Scott Baldridge, and Paul Kirk},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911183724217564776},
  booktitle={Journal of Differential Geometry},
  volume={82},
  number={2},
  pages={317-361},
  year={2009},
}
Scott Baldridge, and Paul Kirk. CONSTRUCTIONS OF SMALL SYMPLECTIC 4-MANIFOLDS USING LUTTINGER SURGERY. 2009. Vol. 82. In Journal of Differential Geometry. pp.317-361. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911183724217564776.
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