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Bordered contact instantons and their Fredholm theory and generic transversalities

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arxiv 2209.03548 v3 pith:PHYUU5S2 submitted 2022-09-08 math.SG

Yong-Geun Oh This is my paper · ORCID
classification math.SG
keywords borderedboundarycontactgenericinstantonsconditionestablishfredholm
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In this article, we first establish the Fredholm theory for the bordered contact instantons defined on the punctured Riemann surfaces with prescribed asymptotic condition near the boundary punctures. We then prove the generic mapping transversality under the perturbation of Legendrian boundary condition. We also establish their generic (0-jet) evaluation transversality results of their moduli space under the perturbations of CR almost complex structures and of Legendrian boundary conditions. These are fundamental ingredients of the construction of the moduli space of bordered contact instantons and their applications.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quantitative contact Hamiltonian dynamics

    math.SG 2025-07 conditional novelty 7.0 of 10

    Contact spectral invariants are constructed from contact Hamiltonian Floer homology and used to prove rigidity theorems for contact manifolds.

  2. Generic jet evaluation transversality of contact instantons against contact distribution

    math.SG 2025-01 conditional novelty 6.0 of 10

    For a generic almost complex structure adapted to a contact form, the moduli space of contact instantons with a tangency to the contact distribution is smooth with the expected dimension.

  3. Rational contact instantons and Legendrian Fukaya category

    math.SG 2024-11 reject novelty 6.0 of 10

    A filtered A-infinity category, the Legendrian CI Fukaya category, is defined using moduli spaces of contact instantons with Reeb chord asymptotics.

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