A Partial Ordering on Slices of Planar Lagrangians

Details A Partial Ordering on Slices of Planar Lagrangians A Partial Ordering on Slices of Planar Lagrangians

2008-08-08

arxiv.org/abs/0808.1281v1

Mathematics

Symplectic Geometry

17 pages, 4 figures; to appear in the Arnold Volume of the Journal of Fixed Point Theory and Applications

Scientific paper

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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