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.
Wendl,Lectures on symplectic field theory, arXiv:1612.01009, to appear in the EMS Lectures in Mathematics series
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abstract
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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Elementary spectral invariants simplify embedded contact homology spectral invariants for contact three-manifolds and can be used to prove some results on periodic orbits of Reeb vector fields, with the remaining results requiring the full ECH invariants.
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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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Elementary spectral invariants and three-dimensional Reeb dynamics
Elementary spectral invariants simplify embedded contact homology spectral invariants for contact three-manifolds and can be used to prove some results on periodic orbits of Reeb vector fields, with the remaining results requiring the full ECH invariants.