Laminations as systolic phase transition

We study a phase transition associated with the property of systolic freedom for families of metrics on 3-manifolds. Given a sequence of minimizing nonseparating surfaces in a systolically free sequence of metrics, we describe a certain accumulation phenomenon. The latter can be captured in the limit by a dichotomy property for the limiting minimal lamination. Such a dichotomy can thus be seen as the essense of systolic freedom with integer coeecients. We provide a related clariication, both of M. Gromov's seminal 4-dimensional example of systolic freedom, and of its 3-dimensional local version developed by I. Babenko and the author with the aim of generalizing systolic freedom to arbitrary manifolds. Our clariication is in terms of the geometry of a speciic 2-dimensional complex imbedded inside them. A classical result of H. Federer's for codimension 1 currents in manifolds fails to hold for this 2-complex, accounting for systolic freedom.