UC San Diego

We develop some foundational results in a higher dimensional foliated Mori theory, and

show how these results can be used to prove a structure theorem for the Kleiman-Mori cone

of curves in terms of the numerical properties of $K_{\cal F}$ for rank 2 foliations

on threefolds. We also make progress

toward realizing a minimal model program for rank 2 foliations on threefolds.