Luttinger surgery along Lagrangian tori and non-isotopy for singular symplectic plane curves

By D. Auroux, Simon Donaldson, L. Katzarkov. 2002

122 citations recorded by the source corpus.

Abstract. We discuss the properties of a certain type of Dehn surgery along a Lagrangian torus in a symplectic 4-manifold, known as Luttinger's surgery, and use this construction to provide a purely topological interpretation of a non-isotopy result for symplectic plane curves with cusp and node singularities due to Moishezon [9].

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2f0b9b4a3e74c5bf351b0655ece0996b1d49bf52

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Complex surfaces of general type: some recent progress (2006, background): “e has a ﬁnite number of connected components. These two statements together give a negative answer to the above cited problem of Chisini. The examples of Moishezon have been recently reinterpreted in [ADK03], with a simpler treatment, in terms of symplectic surgeries. 2) In fact, as conjectured by M”
Exotic smooth structures on small 4-manifolds with odd signatures (2007, unknown): “[5, 19]) and a single m torus surgery on Σ2 × Σn.”
Constructing infinitely many smooth structures on small 4‐manifolds (2007, background): “ery n ≥ 1. 2.4. Luttinger surgery. Luttinger surgery is a special case of p/q surgery on a self-intersection zero torus Λ described in the previous subsection. It was ﬁrst studied in [Lu] and then in [ADK] in a more general setting. Assume that X is a symplectic 4-manifold with a symplectic form ω, ”
Strongly fillable contact manifolds and $J$-holomorphic foliations (2008, unknown): “ng the zero section in T2×R2. The following is a special case of the surgery along a Lagrangian 2–torus in a symplectic 4–manifold introduced by Luttinger in [Lut95]; our formulation is borrowed from [ADK03]. For r > 0, let Kr = T2 × [−r,r] × [−r,r]. Choose constants σ := (c,k1,k2) ∈ (0,∞) × Z2 a”