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Elements of the Lagrangian Whitney trick

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Abstract

We investigate the possibility of a Lagrangian Whitney trick, a process to remove a pair of intersection points of a self-transverse Lagrangian immersion by a homotopy through Lagrangian immersions. There is a model for which a Lagrangian Whitney trick with compact support works assuming the model satisfies an area-capacity condition. Reduction of more general cases to the model, not necessarily fulfilling the area-capacity requirement, is possible if the given pair of double points admits a suitable symplectic disc and a certain Maslov-Viterbo index is 1. We look into an example to see the actualities of the Maslov-Viterbo index and the area-capacity conditions.

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Correspondence to Yanghyun Byun.

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The authors would like to thank the anonymous referee whose suggestions improved remarkably the exposition of the paper. This work was supported by the grant no.R01-2000-000-00004-0 from Korea Science & Engineering Foundation.

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Byun, Y., Joe, D., Seog Ryu, J. et al. Elements of the Lagrangian Whitney trick . Math. Z. 245, 435–453 (2003). https://doi.org/10.1007/s00209-003-0535-x

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