Klein bottles in genus two 3-manifolds
Let M be a closed 3-manifold with Heegaard splitting of genus g. Consider the following question: If M contains an incompressible surface S, does M contain an incompressible surface T homeomorphic to S and such that T intersects the Heegaard surface in a single circle? This was first answered affirmatively by W. Haken if S is a 2-sphere. M. Ochiai gave an affirmative answer for S a 2-sided projective plane and T. Kobayashi for S a non-separating torus and \(g=2\). In the paper under review the author gives an affirmative answer for S a Klein bottle, M orientable, and \(g=2\). As an application, orientable 3-manifolds of genus 2 that contain a Klein bottle are classified. (In his forthcoming thesis at Florida State University, I. Cardona has obtained the same results including non- orientable 3-manifolds.)
scientific article; zbMATH DE number 3942515