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arXiv · 2301.08311

Floer Cohomology and Higher Mutations

Soham Chanda
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Abstract

We extend the construction of higher mutation as introduced in Pascaleff-Tonkonog to local higher mutation, which is applicable to a larger class of monotone Lagrangians. In two-dimensional Lagrangians, local higher mutation is the same as performing a Lagrangian anti-surgery in the sense of Haug followed by a Lagrangian surgery. We prove that up to a change of local systems, the Lagrangian intersection Floer cohomology of a pair of Lagrangians is invariant under local mutation. This result generalizes the wall-crossing formula in Pascaleff-Tonkonog. For two-dimensional Lagrangians, this result agrees with the invariance result in Palmer-Woodward.

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Soham Chanda. 2023-01-19. Floer Cohomology and Higher Mutations. https://arxiv.org/abs/2301.08311

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