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Lectures on Symplectic Field Theory

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arxiv 1612.01009 v2 pith:HIFJZFFX submitted 2016-12-03 math.SG

Chris Wendl This is my paper · ORCID
classification math.SG
keywords symplectictheorycontactfieldanalyticalapplicationsbookcontactomorphism
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This is the preliminary manuscript of a book on symplectic field theory based on a lecture course for PhD students given in 2015-16. It covers the essentials of the analytical theory of punctured pseudoholomorphic curves, taking the opportunity to fill in gaps in the existing literature where necessary, and then gives detailed explanations of a few of the standard applications in contact topology such as distinguishing contact structures up to contactomorphism and proving symplectic non-fillability.

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Cited by 6 Pith papers

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

  1. Bourgeois contact structures: tightness, fillability and applications

    math.SG 2019-08 accept novelty 8.0 of 10

    Bourgeois contact 5-manifolds are universally tight, strong fillability of Bourgeois manifolds forces homological injections, and the unit cotangent bundle of the n-torus has a unique aspherical strong filling.

  2. Relative symplectic cohomology in complex projective spaces

    math.SG 2026-06 unverdicted novelty 6.0 of 10

    Explicit computation of relative symplectic cohomology over the Novikov ring for balls in CP^n via J-shaped Hamiltonians and Morse-Bott cascades with cascades, producing new stable displacement energy estimates.

  3. Unknottedness of symplectic submanifold fillings

    math.SG 2025-06 conditional novelty 6.0 of 10

    Symplectic fillings of the standard codimension-2 contact sphere in a symplectic ball are smoothly isotopic to the standard linear disk.

  4. Counting Minimal Tori In Riemannian Manifolds

    math.DG 2024-12 reject novelty 6.0 of 10

    An integer-valued count of immersed minimal tori in closed Riemannian manifolds of dimension at least 8 is introduced and asserted to be invariant under metric perturbations.

  5. Categorical mirror symmetry on cohomology for a complex genus 2 curve

    math.SG 2019-08 conditional novelty 6.0 of 10

    The paper constructs the SYZ mirror Landau-Ginzburg model of a genus 2 curve and proves a cohomology-level homological mirror symmetry embedding of line bundles into a new Fukaya-Seidel category of a non-exact fibration.

  6. An Abstract Perturbation Theorem for Compact Moduli Spaces

    math.SG 2026-06 unverdicted novelty 5.5 of 10

    An abstract perturbation theorem turns compact zero sets of Fredholm sections into nearby compact smooth manifolds (preserving transverse loci), enabling cobordisms and a re-proof of Schwarz's action spectrum result.

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