Add to ORKGclosed essential surface in M with g.F / 1 which cuts M into M1 and M2. In the present paper, we show the following theorem: Suppose that there is no essential surface with boundary.Qi; @Qi / in.Mi;F / satisfying .Qi/>2Cg.F /2g.Mi /, i D 1; 2. Then g.M /Dg.M1/Cg.M2/g.F /. As a consequence, we further show that if Mi has a Heegaard splitting Vi[SiWi with distance D.Si/2g.Mi/g.F /, i D 1; 2, then g.M /D g.M1/Cg.M2/g.F /. The main results follow from a new technique which is a stronger version of Schultens’ Lemma. 57M99, 57N10; 57M2
Abstract. Kevin Hartshorn showed that if a three-dimensional manifold M admits a Heegaard surface Σ ...
AbstractCerf theory can be used to compare two strongly irreducible Heegaard splittings of the same ...
Haken showed that the Heegaard splittings of reducible 3-manifolds are reducible, that is, ...
closed essential surface in M with g.F / 1 which cuts M into M1 and M2. In the present paper, we s...
AbstractLet M be a compact orientable irreducible 3-manifold, F be an essential non-separating close...
We address a special case of the Stabilization Problem for Heegaard splittings, establishing an uppe...
AbstractLet M be a compact orientable 3-manifold, and let F be a separating (resp. non-separating) i...
Let M be a compact orientable 3-manifold, and let F be a separating (resp. non-separating) incompres...
We show that if two 3–manifolds with toroidal boundary are glued via a “sufficiently complicated &qu...
We describe probably the simplest 3-manifold which contains closed separating incompressible surface...
Given a Heegaard splitting and an incompressible surface S and a Heegaard splitting of an irreducibl...
A Heegaard splitting of an open 3–manifold is the partition of the manifold into two non-compact han...
AbstractIf a Heegaard splitting of a nonsufficiently large 3-manifold has the property that there ex...
Abstract. We show that subsurfaces of a Heegaard surface for which the relative Hempel distance of t...
We introduce the notions of Heegaard splittings and thin multiple Heegaard splittings of 1-submanifo...
Abstract. Kevin Hartshorn showed that if a three-dimensional manifold M admits a Heegaard surface Σ ...
AbstractCerf theory can be used to compare two strongly irreducible Heegaard splittings of the same ...
Haken showed that the Heegaard splittings of reducible 3-manifolds are reducible, that is, ...
closed essential surface in M with g.F / 1 which cuts M into M1 and M2. In the present paper, we s...
AbstractLet M be a compact orientable irreducible 3-manifold, F be an essential non-separating close...
We address a special case of the Stabilization Problem for Heegaard splittings, establishing an uppe...
AbstractLet M be a compact orientable 3-manifold, and let F be a separating (resp. non-separating) i...
Let M be a compact orientable 3-manifold, and let F be a separating (resp. non-separating) incompres...
We show that if two 3–manifolds with toroidal boundary are glued via a “sufficiently complicated &qu...
We describe probably the simplest 3-manifold which contains closed separating incompressible surface...
Given a Heegaard splitting and an incompressible surface S and a Heegaard splitting of an irreducibl...
A Heegaard splitting of an open 3–manifold is the partition of the manifold into two non-compact han...
AbstractIf a Heegaard splitting of a nonsufficiently large 3-manifold has the property that there ex...
Abstract. We show that subsurfaces of a Heegaard surface for which the relative Hempel distance of t...
We introduce the notions of Heegaard splittings and thin multiple Heegaard splittings of 1-submanifo...
Abstract. Kevin Hartshorn showed that if a three-dimensional manifold M admits a Heegaard surface Σ ...
AbstractCerf theory can be used to compare two strongly irreducible Heegaard splittings of the same ...
Haken showed that the Heegaard splittings of reducible 3-manifolds are reducible, that is, ...