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Unobstructed Lagrangian cobordism groups of surfaces
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abstract
We study Lagrangian cobordism groups of closed symplectic surfaces of genus $g \geq 2$ whose relations are given by unobstructed, immersed Lagrangian cobordisms. Building upon work of Abouzaid and Perrier, we compute these cobordism groups and show that they are isomorphic to the Grothendieck group of the derived Fukaya category of the surface. The proofs rely on techniques from two-dimensional topology to construct cobordisms that do not bound certain types of holomorphic polygons.
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Fourier transforms and a filtration on the Lagrangian cobordism group of tori
For polarized tropical affine tori, the fibered Lagrangian cobordism group carries a parallelotope filtration that vanishes after n+1 steps, and the associated symplectic Fourier transform mirrors Mukai's transform.
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