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Results 1 - 10
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218
ON CLASSIFICATION OF HEEGAARD SPLITTINGS AND TRIANGULATIONS
, 1997
"... In this paper we consider Heegaard splittings of 3-manifolds. By using Gabai’s concept of thin position on the 1-skeleton of some polyhedral decomposition, together with Casson-Gordon’s concept of strong irreducibility, we prove the Main Theorem (4.0). This theorem will allow us to classify the Heeg ..."
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In this paper we consider Heegaard splittings of 3-manifolds. By using Gabai’s concept of thin position on the 1-skeleton of some polyhedral decomposition, together with Casson-Gordon’s concept of strong irreducibility, we prove the Main Theorem (4.0). This theorem will allow us to classify
ON NON-COMPACT HEEGAARD SPLITTINGS
, 2006
"... Abstract. A Heegaard splitting of an open 3-manifold is the partition of the manifold into two non-compact handlebodies which intersect on their common boundary. This paper proves several non-compact analogues of theorems about compact Heegaard splittings. The main theorem is: if N is a compact, con ..."
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Abstract. A Heegaard splitting of an open 3-manifold is the partition of the manifold into two non-compact handlebodies which intersect on their common boundary. This paper proves several non-compact analogues of theorems about compact Heegaard splittings. The main theorem is: if N is a compact
Flipping and stabilizing Heegaard splittings
"... Abstract. We show that the number of stabilizations needed to interchange the handlebodies of a Heegaard splitting of a closed 3-manifold by an isotopy is bounded below by the smaller of twice its genus or half its Hempel distance. This is a combinatorial version of a proof by Hass, Thompson and Thu ..."
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Cited by 6 (3 self)
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Abstract. We show that the number of stabilizations needed to interchange the handlebodies of a Heegaard splitting of a closed 3-manifold by an isotopy is bounded below by the smaller of twice its genus or half its Hempel distance. This is a combinatorial version of a proof by Hass, Thompson
Transverse Heegaard splittings
- Michigan Math. J
, 1997
"... Abstract. Following an example discovered by John Berge [Be2], we show that there is a 4-component link L ⊂ (S1×S2)#(S1×S2) so that, generically, the result of Dehn surgery on L is a 3-manifold with two inequivalent genus 2 Heegaard splittings, and each of these Heegaard splittings is of Hempel dist ..."
Abstract
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Cited by 5 (2 self)
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Abstract. Following an example discovered by John Berge [Be2], we show that there is a 4-component link L ⊂ (S1×S2)#(S1×S2) so that, generically, the result of Dehn surgery on L is a 3-manifold with two inequivalent genus 2 Heegaard splittings, and each of these Heegaard splittings is of Hempel
HEEGAARD SPLITTINGS AND THE PANTS COMPLEX
, 2005
"... Abstract. We define integral measures of complexity for Heegaard splittings based on the graph dual to the curve complex and on the pants complex defined by Hatcher and Thurston. As the Heegaard splitting is stabilized, the sequence of complexities turns out to converge to a non-trivial limit depend ..."
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Cited by 2 (1 self)
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Abstract. We define integral measures of complexity for Heegaard splittings based on the graph dual to the curve complex and on the pants complex defined by Hatcher and Thurston. As the Heegaard splitting is stabilized, the sequence of complexities turns out to converge to a non-trivial limit
On p-symmetric Heegaard splittings
- J. Knot Theory Ramifications
"... We show that every p-fold strictly-cyclic branched covering of a b-bridge link in S 3 admits a p-symmetric Heegaard splitting – in the sense of Birman and Hilden – of genus g = (b −1)(p −1). This gives a complete converse of one of the results of the two authors. Moreover, we introduce the concept o ..."
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Cited by 1 (1 self)
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We show that every p-fold strictly-cyclic branched covering of a b-bridge link in S 3 admits a p-symmetric Heegaard splitting – in the sense of Birman and Hilden – of genus g = (b −1)(p −1). This gives a complete converse of one of the results of the two authors. Moreover, we introduce the concept
Heegaard splittings of twisted bundles
, 2006
"... Abstract. We characterize Heegaard splittings of twisted I-bundles over closed nonorientable surfaces and prove that there is only one irreducible splitting, which is obtained by taking a boundary parallel surface and adding a vertical 1-handle. Then we use the result to prove that irreducible Heega ..."
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Abstract. We characterize Heegaard splittings of twisted I-bundles over closed nonorientable surfaces and prove that there is only one irreducible splitting, which is obtained by taking a boundary parallel surface and adding a vertical 1-handle. Then we use the result to prove that irreducible
Closed Braids and Heegaard Splittings
- in AMS/IP Studies in Advanced Mathematics 24, Amer. Math Society and International
, 2001
"... In this note we will be investigating a strategy for constructing 3-manifolds that have multiple strongly irreducible Heegaard splittings that are not equivalent. This strategy combines techiques involving framed links and a calculus on closed braids developed by Joan Birman and the author. 1 In ..."
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Cited by 2 (2 self)
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In this note we will be investigating a strategy for constructing 3-manifolds that have multiple strongly irreducible Heegaard splittings that are not equivalent. This strategy combines techiques involving framed links and a calculus on closed braids developed by Joan Birman and the author. 1
STABILIZATION OF HEEGAARD SPLITTINGS
, 802
"... Abstract. For each g ≥ 2 there is a 3-manifold with two genus g Heegaard splittings that require g stabilizations to become equivalent. Previously known examples required at most one stabilization. Control of families of Heegaard surfaces is obtained through a deformation to harmonic maps. 1. ..."
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Cited by 14 (0 self)
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Abstract. For each g ≥ 2 there is a 3-manifold with two genus g Heegaard splittings that require g stabilizations to become equivalent. Previously known examples required at most one stabilization. Control of families of Heegaard surfaces is obtained through a deformation to harmonic maps. 1.
Results 1 - 10
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218
