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Pseudoholomorphic Quilts

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arxiv 0905.1369 v3 pith:24ROTC5G submitted 2009-05-09 math.SG math.GT

Katrin Wehrheim , Chris Woodward This is my paper · ORCID
classification math.SGmath.GT
keywords lagrangianpseudoholomorphicapplicationarisingassociatedcollectionsconditionsconstruct
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We define relative Floer theoretic invariants arising from 'quilted pseudo-holomorphic surfaces': Collections of pseudoholomorphic maps to various target spaces with 'seam conditions' in Lagrangian correspondences. As application we construct a morphism on quantum homology associated to any monotone Lagrangian correspondence.

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  1. Fourier transforms and a filtration on the Lagrangian cobordism group of tori

    math.SG 2024-11 conditional novelty 6.0 of 10

    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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