Limits of incompressible surfaces

AbstractOne can embed arbitrarily many disjoint, non-parallel, non-boundary parallel, incompressible surfaces in any three manifold with at least one boundary component of genus two or greater (Howards, 1998). This paper proves the contrasting, but not contradictory result that although one can sometimes embed arbitrarily many surfaces in a 3-manifold it is impossible to ever embed an infinite number of such surfaces in any compact, orientable 3-manifold M