Lagrangian cobordism and tropical curves
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.
Keywords
Cite
@article{arxiv.1805.07924,
title = {Lagrangian cobordism and tropical curves},
author = {Nick Sheridan and Ivan Smith},
journal= {arXiv preprint arXiv:1805.07924},
year = {2020}
}
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