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Mathematics > Symplectic Geometry

arXiv:1805.07924 (math)
[Submitted on 21 May 2018 (v1), last revised 17 Sep 2020 (this version, v3)]

Title:Lagrangian cobordism and tropical curves

Authors:Nick Sheridan, Ivan Smith
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Abstract:We study a cylindrical Lagrangian cobordism group for Lagrangian torus fibres in symplectic manifolds which are the total spaces of smooth Lagrangian torus fibrations. We use ideas from family Floer theory and tropical geometry to obtain both obstructions to and constructions of cobordisms; in particular, we give examples of symplectic tori in which the cobordism group has no non-trivial cobordism relations between pairwise distinct fibres, and ones in which the degree zero fibre cobordism group is a divisible group. The results are independent of but motivated by mirror symmetry, and a relation to rational equivalence of 0-cycles on the mirror rigid analytic space.
Comments: 56 pages; 10 figures. Version 2: minor attributional clarifications and bibliographic changes. Version 3: 44 pages. Text streamlined and other minor changes. This is the final version, to appear in Crelle's journal
Subjects: Symplectic Geometry (math.SG); Algebraic Geometry (math.AG)
MSC classes: 53D35, 53D37, 14T05, 14C25
Cite as: arXiv:1805.07924 [math.SG]
  (or arXiv:1805.07924v3 [math.SG] for this version)
  https://doi.org/10.48550/arXiv.1805.07924

Submission history

From: Ivan Smith [view email]
[v1] Mon, 21 May 2018 07:29:37 UTC (86 KB)
[v2] Thu, 13 Sep 2018 14:57:40 UTC (87 KB)
[v3] Thu, 17 Sep 2020 09:21:29 UTC (99 KB)
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