7 M ay 2 00 8 Geometry and topology of the quasi - plane Szekeres model

Geometrical and topological properties of the quasi-plane Szekeres model and of the plane symmetric dust model are discussed. Some related comments on the quasihyperbolical model are made. These properties include: (1) The pattern of expansion in the plane symmetric case, and the Newtonian model that imitates it; (2) The possibility of toroidal topology of the t = const sections in the plane symmetric model; (3) The absence of apparent horizons in the quasi-plane and quasi-hyperbolic models (they are globally trapped); (4) Description of the toroidal topology in the Szekeres coordinates; (5) Consequences of toroidal topology in the nonsymmetric quasi-plane model; (6) Avoidance of shell crossings in the toroidal model; (7) Interpretation of the mass function in the quasi-plane model, with the toroidal and with the infinite space.