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229
The asymptotic behaviour of Heegaard genus
, 2004
"... Heegaard splittings have recently been shown to be related to a number of important conjectures in 3manifold theory: the virtually Haken conjecture, the positive virtual b1 conjecture and the virtually fibred conjecture [3]. Of particular importance is the rate at which the Heegaard genus of finite ..."
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Cited by 11 (1 self)
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Heegaard splittings have recently been shown to be related to a number of important conjectures in 3manifold theory: the virtually Haken conjecture, the positive virtual b1 conjecture and the virtually fibred conjecture [3]. Of particular importance is the rate at which the Heegaard genus
ON THE HEEGAARD GENUS OF CONTACT 3MANIFOLDS
"... ABSTRACT. It is wellknown that Heegaard genus is additive under connected sum of 3manifolds. We show that Heegaard genus of contact 3manifolds is not necessarily additive under contact connected sum. We also prove some basic properties of the contact genus (a.k.a. open book genus [8]) of 3manif ..."
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ABSTRACT. It is wellknown that Heegaard genus is additive under connected sum of 3manifolds. We show that Heegaard genus of contact 3manifolds is not necessarily additive under contact connected sum. We also prove some basic properties of the contact genus (a.k.a. open book genus [8]) of 3
Degeneration of Heegaard genus, a survey
 In Workshop on Heegaard Splittings
, 2007
"... Abstract. We survey known (and unknown) results about the behavior of Heegaard genus of 3manifolds constructed via various gluings. The constructions we consider are (1) gluing together two 3manifolds with incompressible boundary, (2) gluing together the boundary components of surface × I, and (3) ..."
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Cited by 1 (0 self)
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Abstract. We survey known (and unknown) results about the behavior of Heegaard genus of 3manifolds constructed via various gluings. The constructions we consider are (1) gluing together two 3manifolds with incompressible boundary, (2) gluing together the boundary components of surface × I, and (3
THE HEEGAARD GENUS OF AMALGAMATED 3MANIFOLDS
, 2003
"... When studying Haken 3manifolds, one is led naturally to the following construction: the amalgamation of two 3manifolds M and M ′ via a homeomorphism between their boundaries. In this paper, we study the behaviour of Heegaard genus under this operation. We show that, provided the gluing homeomorphi ..."
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Cited by 19 (0 self)
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When studying Haken 3manifolds, one is led naturally to the following construction: the amalgamation of two 3manifolds M and M ′ via a homeomorphism between their boundaries. In this paper, we study the behaviour of Heegaard genus under this operation. We show that, provided the gluing
The Heegaard genus of bundles over S¹
, 2007
"... This paper explores connections between Heegaard genus, minimal surfaces, and pseudoAnosov monodromies. Fixing a pseudoAnosov map φ and an integer n, let Mn be the 3–manifold fibered over S 1 with monodromy φ n. JH Rubinstein showed that for a large enough n every minimal surface of genus at most ..."
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Cited by 1 (0 self)
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This paper explores connections between Heegaard genus, minimal surfaces, and pseudoAnosov monodromies. Fixing a pseudoAnosov map φ and an integer n, let Mn be the 3–manifold fibered over S 1 with monodromy φ n. JH Rubinstein showed that for a large enough n every minimal surface of genus at most
Alternate Heegaard genus bounds distance
 GEOM. AND TOPOLOGY
, 2006
"... Suppose M is a compact orientable irreducible 3–manifold with Heegaard splitting surfaces P and Q. Then either Q is isotopic to a possibly stabilized or boundarystabilized copy of P or the distance d.P / 2genus.Q/. More generally, if P and Q are bicompressible but weakly incompressible connected clo ..."
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Cited by 48 (3 self)
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Suppose M is a compact orientable irreducible 3–manifold with Heegaard splitting surfaces P and Q. Then either Q is isotopic to a possibly stabilized or boundarystabilized copy of P or the distance d.P / 2genus.Q/. More generally, if P and Q are bicompressible but weakly incompressible connected
Heegaard genus formula for Haken manifolds
"... Suppose M is a compact orientable 3manifold and Q ⊂ M a properly embedded orientable boundary incompressible essential surface. Denote the completions of the components of M − Q with respect to the path metric by M 1,..., M k. Denote the smallest possible genus of a Heegaard splitting of M, or M j ..."
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Cited by 7 (1 self)
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Suppose M is a compact orientable 3manifold and Q ⊂ M a properly embedded orientable boundary incompressible essential surface. Denote the completions of the components of M − Q with respect to the path metric by M 1,..., M k. Denote the smallest possible genus of a Heegaard splitting of M, or M j
Quantum invariants provide sharp Heegaard genus bounds
, 801
"... Using Seifert fibered threemanifold examples of Boileau and Zieschang, we demonstrate that the ReshetikhinTuraev quantum invariants may be used to provide a sharp lower bound on the Heegaard genus which is strictly larger than the rank of the fundamental group. 1 ..."
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Cited by 1 (1 self)
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Using Seifert fibered threemanifold examples of Boileau and Zieschang, we demonstrate that the ReshetikhinTuraev quantum invariants may be used to provide a sharp lower bound on the Heegaard genus which is strictly larger than the rank of the fundamental group. 1
Results 1  10
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229