TORUS HOMEOMORPHISMS WHOSE ROTATION SETS HAVE EMPTY INTERIOR

Let F be a lift of a homeomorphism f : T-2 --> T-2 homotopic to the id entity. We assume that the rotation set rho(F) is a line segment with irrational slope. In this paper we use the fact that T-2 is necessaril y chain transitive under f if f has no periodic points to show that if upsilon is an element of rho(F) is a rational point, then there is a periodic point x is an element of T2 such that upsilon is its rotation vector.