2002/01/14 by Yoav Moriah, Moriah, Yoav
Mathematics · #Advanced Operator Algebra Research #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT
paper · pdf · doi:10.48550/arxiv.math/0201115
13 pages 3 figures. Will appear in Topology and its Applications
arxiv created 2002/11/26 · arxiv updated 2009/11/30
In this paper it is shown that manifolds admitting minimal genus weakly reducible but irreducible Heegaard splittings contain an essential surface. This is an extension of a well known theorem of Casson-Gordon to manifolds with non-empty boundary. The situation for non-minimal genus Heegaard splittings is also investigated and it is shown that boundary stabilizations are stabilizations for manifolds which are boundary primitive.