Topologically Distinct Lagrangian and Symplectic Fillings

Cao, Chang; Gallup, Nathaniel; Hayden, Kyle; Sabloff, Joshua M.

doi:10.48550/arxiv.1307.7998

Cited by 1 publication

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“…n = 3, 5, 6, 12, even up to diffeomorphism, [34]. As it was pointed out to me by O. Lazarev, one can show using methods of [9] that certain exotic T * S n may contain several not homotopy equivalent regular closed exact Lagrangian submanifolds. Problem 6.3.…”

Section: Symplectic Topology Of Weinstein Manifoldsmentioning

confidence: 93%

Weinstein manifolds revisited

Eliashberg¹

2018

Proceedings of Symposia in Pure Mathematics

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This is a very biased and incomplete survey of some basic notions, old and new results, as well as open problems concerning Weinstein symplectic manifolds. Weinstein manifolds, domains, cobordismsWe begin with a notion of a Liouville domain. Let (X, ω) be a 2n-dimensional compact symplectic manifold with boundary equipped with an exact symplectic form ω. A Liouville structure on (X, ω) is a choice of a primitive λ, dλ = ω, called Liouville form such that λ| ∂X is a contact form and the orientation of ∂X by the form λ ∧ dλ n−1 | ∂X coincides with its orientation as the boundary of symplectic manifold (X, ω). The vector field Z, that is ω-dual to λ, i.e. ι(Z)ω = λ, is also called Liouville. It satisfies the condition L Z ω = ω which means that its flow is conformally symplectically expanding. The contact boundary condition is equivalent to the outward transversality of Z to ∂X. A Liouville domain X can always be completed to a Liouville manifold X by attaching a cylindrical end:and extending λ to X as equal to e s (λ| ∂X ) on the attached end. We will be constantly going back and forth between these two tightly related notions of Liouville domains and Liouville manifolds.Given a Liouville structure L = (X, ω, Z) we say that a Liouville structure L = (X , ω, Z) is obtained by a radial deformation from L if there exists a function h : *

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Section: Symplectic Topology Of Weinstein Manifoldsmentioning

confidence: 93%

Weinstein manifolds revisited

Eliashberg¹

2018

Proceedings of Symposia in Pure Mathematics

View full text Add to dashboard Cite

show abstract

Topologically Distinct Lagrangian and Symplectic Fillings

Cited by 1 publication

References 16 publications

Weinstein manifolds revisited

Weinstein manifolds revisited

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