scholarly journals Explicit Dehn filling and Heegaard splittings

2013 ◽  
Vol 21 (3) ◽  
pp. 625-650 ◽  
Author(s):  
David Futer ◽  
Jessica S. Purcell
Keyword(s):  
Heegaard Splittings ◽  
Dehn Filling

scholarly journals LIFTED HEEGAARD SURFACES AND VIRTUALLY HAKEN MANIFOLDS

2012 ◽  
Vol 21 (08) ◽  
pp. 1250073
Author(s):  
YU ZHANG
Keyword(s):  
New York ◽  
Heegaard Splittings ◽  
Finite Cover ◽  
Incompressible Surface ◽  
Dehn Filling ◽  
Base Manifold ◽  
Heegaard Surfaces ◽  
Heegaard Surface

In this paper, we give infinitely many non-Haken hyperbolic genus three 3-manifolds each of which has a finite cover whose induced Heegaard surface from some genus three Heegaard surface of the base manifold is reducible but can be compressed into an incompressible surface. This result supplements [A. Casson and C. Gordon, Reducing Heegaard splittings, Topology Appl. 27 (1987) 275–283] and extends [J. Masters, W. Menasco and X. Zhang, Heegaard splittings and virtually Haken Dehn filling, New York J. Math. 10 (2004) 133–150].

Local uniqueness of certain geodesics related to Heegaard splittings

2018 ◽  
Vol 27 (09) ◽  
pp. 1842003
Author(s):  
Liang Liang ◽  
Fengling Li ◽  
Fengchun Lei ◽  
Jie Wu
Keyword(s):  
Heegaard Splitting ◽  
Sufficient Condition ◽  
Heegaard Splittings ◽  
Local Uniqueness ◽  
Uniqueness Property

Suppose [Formula: see text] is a Heegaard splitting and [Formula: see text] is an essential separating disk in [Formula: see text] such that a component of [Formula: see text] is homeomorphic to [Formula: see text], [Formula: see text]. In this paper, we prove that if there is a locally complicated simplicial path in [Formula: see text] connecting [Formula: see text] to [Formula: see text], then the geodesic connecting [Formula: see text] to [Formula: see text] is unique. Moreover, we give a sufficient condition such that [Formula: see text] is keen and the geodesic between any pair of essential disks on the opposite sides has local uniqueness property.

The amalgamation of high distance Heegaard splittings is always efficient

2008 ◽  
Vol 341 (3) ◽  
pp. 707-715 ◽  
Author(s):  
Tsuyoshi Kobayashi ◽  
Ruifeng Qiu
Keyword(s):  
Heegaard Splittings

Minimal Plat Representations of Prime Knots and Links are not Unique

1976 ◽  
Vol 28 (1) ◽  
pp. 161-167 ◽  
Author(s):  
José M. Montesinos
Keyword(s):  
Infinite Family ◽  
Equivalence Classes ◽  
Covering Space ◽  
Heegaard Splittings ◽  
Cyclic Covering ◽  
Knots And Links

Letdenote the 2-fold cyclic covering space branched over a linkLin S3. We wish to describe an infinite family of prime knots and links in which each memberLexhibits two minimal 6-plat representations, where the associated Heegaard splittings ofare minimal and inequivalent. Thus each knot or link of that family admits at least two equivalence classes of 6-plat representations which are minimal.

scholarly journals One-sided Heegaard splittings of ℝP3

2006 ◽  
Vol 6 (3) ◽  
pp. 1319-1330 ◽  
Author(s):  
Loretta Bartolini ◽  
J Hyam Rubinstein
Keyword(s):  
Heegaard Splittings
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