IRREDUCIBLE 3-MANIFOLDS WHICH MAY CONTAIN TWO-SIDED PROJECTIVE PLANES

A description is obtained for the homeotopy group (the group of iso-topy classes of homeomorphisms) of a compact irreducible sufficiently large 3-manifold (which may contain 2-sided projective planes). It is finitely presented, and modulo finite groups is either free, GL(3, Z), or is built up in a certain way by extensions starting from 2-manifold homeotopy groups and finitely generated abelian groups. 0. Introduction. Manifolds containing 2-sided projective planes have been a stumbling block in the study of mappings of 3-manifolds. For orientable sufficiently large 3-manifolds with incompressible boundary (now called Haken 3-manifolds), Waldhausen's [W] sem-inal work provides (except for /-bundles) an isomorphism from th