منابع مشابه
Critical Heegaard Surfaces
In this paper we introduce critical surfaces, which are described via a 1-complex whose definition is reminiscent of the curve complex. Our main result is that if the minimal genus common stabilization of a pair of strongly irreducible Heegaard splittings of a 3-manifold is not critical, then the manifold contains an incompressible surface. Conversely, we also show that if a nonHaken 3-manifold...
متن کاملCritical Heegaard Surfaces and Index 2 Minimal Surfaces
This paper contains the motivation for the study of critical surfaces in [2]. In that paper, the only justification given for the definition of this new class of surfaces is the strength of the results. However, when viewed as the topological analogue to index 2 minimal surfaces, critical surfaces become quite natural.
متن کاملHeegaard Surfaces and the Distance of Amalgamation
Let M1 and M2 be orientable irreducible 3–manifolds with connected boundary and suppose ∂M1 = ∂M2. Let M be a closed 3–manifold obtained by gluing M1 to M2 along the boundary. We show that if the gluing homeomorphism is sufficiently complicated, then M is not homeomorphic to S and all small-genus Heegaard splittings of M are standard in a certain sense. In particular, g(M) = g(M1) + g(M2) − g(∂...
متن کاملPrincipal Curvatures of Fibers and Heegaard Surfaces
We study principal curvatures of fibers and Heeagaard surfaces smoothly embedded in hyperbolic 3-manifolds. It is well known that a fiber or a Heegaard surface in a hyperbolic 3-manifold cannot have principal curvatures everywhere less than one in absolute value. We show that given an upper bound on the genus of a minimally embedded fiber or Heegaard surface and a lower bound on the injectivity...
متن کاملincompressible surfaces and stabilizations of Heegaard splittings
We describe probably the simplest 3-manifold which contains closed separating incompressible surfaces of arbitrarily large genus. Two applications of this observation are given. (1) For any closed, orientable 3-manifold M and any integer m> 0, a surgery on a link inM of at most 2m+1 components will provide a closed, orientable, irreducible 3-manifold containing m disjoint, non-parallel, separat...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1991
ISSN: 0002-9947
DOI: 10.2307/2001640