A Partial Ordering on Slices of Planar Lagrangians

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.

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