Lagrangian cobordism and tropical curves

Nick Sheridan, Ivan Smith

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)N/A
Number of pages45
JournalJournal für die reine und angewandte Mathematik
VolumeN/A
Early online date7 Nov 2020
DOIs
Publication statusE-pub ahead of print - 7 Nov 2020

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