S-Maximal Subgroups of πl(M3)

Abstract

Let M be a compact, connected, irreducible 3-manifold. Let S be a closed, connected, 2-manifold other than the 2-sphere or projective plane. Let f be a map of S into M such thatSuppose for every closed, connected surface S1 and every map g:S1 → M such that(1) is an injection,(1) Then we shall say that the subgroup is a surface maximal or S-maximal subgroup of π1(M). We may also say that the map f is S-maximal.Let M be an irreducible 3-manifold which does not admit any embedding of the projective plane. Then we shall say that M is p2-irreducible. Throughout this paper all spaces will be simplicial complexes and all maps will be piecewise linear.