  We consider the Lorenz equations, a system of three dimensional ordinary
differential equations modeling atmospheric convection. These equations are
chaotic and hard to study even numerically, and so a simpler "geometric model"
has been introduced in the seventies. One of the classical problems in
dynamical systems is to relate the original equations to the geometric model.
This has been achieved numerically by Tucker for the classical parameter
values, and remains open for general values. In this paper we establish
analytically a relation to the geometric model, for a different set of
parameter values that we prove must exist. This is facilitated by finding a
novel way to apply topological tools developed for the study of surface
dynamics to the more intricate case of three dimensional flows.
