Obstructions to the Existence and Squeezing of Lagrangian Cobordisms

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dc.creatorSabloff, Joshua M.
dc.creatorTraynor, Lisa
dc.date2008-08-08
dc.date2008-12-17
dc.date.accessioned2026-07-07T12:13:16Z
dc.date.available2026-07-07T12:13:16Z
dc.descriptionCapacities that provide both qualitative and quantitative obstructions to the existence of a Lagrangian cobordism between two $(n-1)$-dimensional submanifolds in parallel hyperplanes of $\mathbb{R}^{2n}$ are defined using the theory of generating families. Qualitatively, these capacities show that, for example, in $\mathbb R^4$ there is no Lagrangian cobordism between two $\infty$-shaped curves with a negative crossing when the lower end is "smaller". Quantitatively, when the boundary of a Lagrangian ball lies in a hyperplane of $\mathbb{R}^{2n}$, the capacity of the boundary gives a restriction on the size of a rectangular cylinder into which the Lagrangian ball can be squeezed.
dc.description30 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/0808.1274
dc.identifierhttp://arxiv.org/abs/0808.1274
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210790
dc.subjectSymplectic Geometry
dc.subject53D12; 57R17
dc.titleObstructions to the Existence and Squeezing of Lagrangian Cobordisms
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