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arXiv · 0808.1281

A Partial Ordering on Slices of Planar Lagrangians

Phil Eiseman·Jonathan D. Lima·Joshua M. Sabloff·Lisa Traynor
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Abstract

A collection of simple closed curves in $\rr^3$ is called a negative slice if it is the intersection of a flat-at-infinity planar Lagrangian surface and $\{y_2 = a \}$ for some $a < 0$. Examples and non-examples of negative slices are given. Embedded Lagrange cobordisms define a relation on slices and in some (and perhaps all) cases this relation defines a partial order. The set of slices is a commutative monoid and the additive structure has an interesting relationship with the ordering relation.

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Phil Eiseman, Jonathan D. Lima, Joshua M. Sabloff, Lisa Traynor. 2008-08-08. A Partial Ordering on Slices of Planar Lagrangians. https://arxiv.org/abs/0808.1281

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