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Mathematics > Symplectic Geometry

arXiv:1806.03722 (math)
[Submitted on 10 Jun 2018 (v1), last revised 16 Jun 2020 (this version, v2)]

Title:Refined disk potentials for immersed Lagrangian surfaces

Authors:Georgios Dimitroglou Rizell, Tobias Ekholm, Dmitry Tonkonog
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Abstract:We define a refined Gromov-Witten disk potential of self-transverse monotone immersed Lagrangian surfaces in a symplectic 4-manifold as an element in a capped version of the Chekanov--Eliashberg dg-algebra of the singularity links of the double points (a collection of Legendrian Hopf links). We give a surgery formula that expresses the potential after smoothing a double point.
We study refined potentials of monotone immersed Lagrangian spheres in the complex projective plane and find monotone spheres that cannot be displaced from complex lines and conics by symplectomorphisms. We also derive general restrictions on sphere potentials using Legendrian lifts to the contact 5-sphere.
Comments: 65 pages, 11 figures. Revised version with many fixes. More details about the construction of the Fukaya category with refined local systems (Section 6). Computed the full wrapped Floer homology in the case of the self-plumbing of a sphere, i.e. the homology of the derived mult. preproj. algebra of a one vertex loop (Theorem 3.13)
Subjects: Symplectic Geometry (math.SG); Representation Theory (math.RT)
MSC classes: 53D40, 53D42, 57R17
Cite as: arXiv:1806.03722 [math.SG]
  (or arXiv:1806.03722v2 [math.SG] for this version)
  https://doi.org/10.48550/arXiv.1806.03722

Submission history

From: Georgios Dimitroglou Rizell [view email]
[v1] Sun, 10 Jun 2018 20:56:14 UTC (185 KB)
[v2] Tue, 16 Jun 2020 16:41:53 UTC (194 KB)
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