arXiv subjects
Publications and source records attributed to Hugh Nelson Howards.
Given a properly embedded graph Gamma in a ball B and a punctured sphere Sigma properly embedded in B - Gamma, we examine the conditions on Gamma that are necessary to assure that Sigma is boundary parallel.
One 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 [4]. 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.