Limits Of Incompressible Surfaces

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.Comment: 8 pages, Latex, psfig, to be published in Topology and Its Application

Thin position for knots and 3-manifolds

Abstract We prove that for 2-bridge knots and 3-bridge knots in thin position the double branched cover inherits a manifold decomposition in thin position. We also argue that one should not expect this sort of correspondence to hold in general. © 2008 Elsevier B.V. All rights reserved. Keywords: Double branched cover; Bridge position; Thin position; 3-manifold decomposition Preliminaries Thin position for knots was first defined by D. Gabai i

Generating disjoint incompressible surfaces

AbstractWe show that one can embed an arbitrarily large collection of disjoint, incompressible, non-parallel, non-boundary-parallel surfaces in any compact, orientable 3-manifold with at least one boundary component of genus greater than or equal to two.We also provide an answer to the open question, Question III.16, from Jaco's book, Lecture Notes on 3-Manifold Topology