Constructions of small symplectic 4-manifolds using Luttinger surgery

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dc.creatorBaldridge, Scott
dc.creatorKirk, Paul
dc.date2007-03-02
dc.date.accessioned2026-07-07T07:49:54Z
dc.date.available2026-07-07T07:49:54Z
dc.descriptionIn this article we use the technique of Luttinger surgery to produce small examples of simply connected and non-simply connected minimal symplectic 4-manifolds. In particular, we construct: (1) An example of a minimal symplectic 4-manifold that is homeomorphic but not diffeomorphic to CP^2#3(-CP^2) which contains a symplectic surface of genus 2, trivial normal bundle, and simply connected complement and a disjoint nullhomologous Lagrangian torus with the fundamental group of the complement generated by one of the loops on the torus. (2) A minimal symplectic 4-manifold that is homeomorphic but not diffeomorphic to 3CP^2#5(-CP^2) which has two essential Lagrangian tori with simply connected complement. These manifolds can be used to replace E(1) in many known theorems and constructions. Examples in this article include the smallest known minimal symplectic manifolds with abelian fundamental groups including symplectic manifolds with finite and infinite cyclic fundamental group and Euler characteristic 6.
dc.description37 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/math/0703065
dc.identifierhttp://arxiv.org/abs/math/0703065
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124992
dc.subjectGeometric Topology
dc.subjectSymplectic Geometry
dc.subject57R17; 57M05; 54D05
dc.titleConstructions of small symplectic 4-manifolds using Luttinger surgery
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