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arXiv · 1903.01943

Invariance of immersed Floer cohomology under Lagrangian surgery

Joseph Palmer·Chris Woodward
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Abstract

We show that Floer cohomology of an immersed Lagrangian brane is invariant under smoothing of a self-intersection point if the quantum valuation of the weakly bounding cochain vanishes and the Lagrangian has dimension at least two. The chain-level map replaces the two orderings of the self-intersection point with meridianal and longitudinal cells on the handle created by the surgery, and uses a bijection between holomorphic disks developed by Fukaya-Oh-Ohta-Ono. Our result generalizes invariance of potentials for certain Lagrangian surfaces in Dimitroglou-Rizell--Ekholm--Tonkonog, and implies the invariance of Floer cohomology under mean curvature flow with this type of surgery, as conjectured by Joyce.

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Joseph Palmer, Chris Woodward. 2019-03-05. Invariance of immersed Floer cohomology under Lagrangian surgery. https://arxiv.org/abs/1903.01943

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