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Lectures on Symplectic Field Theory
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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 4 Pith papers
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Relative symplectic cohomology in complex projective spaces
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.
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Unknottedness of symplectic submanifold fillings
Symplectic fillings of the standard codimension-2 contact sphere in a symplectic ball are smoothly isotopic to the standard linear disk.
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Counting Minimal Tori In Riemannian Manifolds
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.
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An Abstract Perturbation Theorem for Compact Moduli Spaces
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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