heegaard genus
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2019 ◽  
Vol 28 (02) ◽  
pp. 1950014
Author(s):  
Yang Li ◽  
Guoqiu Yang

Let [Formula: see text] be a compact, connected, orientable closed 3-manifold. Let [Formula: see text] be a disjoint union of incompressible separating tori in [Formula: see text] which cut [Formula: see text] into the submanifolds [Formula: see text]. In the present paper, we show that the Heegaard genus [Formula: see text] of [Formula: see text] is given by [Formula: see text] provided that each [Formula: see text] has a Heegaard splitting [Formula: see text] with Hempel distance [Formula: see text].


2018 ◽  
Vol 12 (02) ◽  
pp. 357-369
Author(s):  
Alessandro Sisto

We give a simple criterion for a Heegaard splitting to yield a Haken manifold. As a consequence, we construct many Haken manifolds, in particular homology spheres, with prescribed properties, namely Heegaard genus, Heegaard distance and Casson invariant. Along the way we give simpler and shorter proofs of the existence of splittings with specified Heegaard distance, originally proven by Ido–Jang–Kobayashi, of the existence of hyperbolic manifolds with prescribed Casson invariant, originally due to Lubotzky–Maher–Wu, and of a result about subsurface projections of disc sets (for which we even get better constants), originally due to Masur–Schleimer.


2017 ◽  
Vol 26 (11) ◽  
pp. 1750063 ◽  
Author(s):  
Kun Du ◽  
Ruifeng Qiu
Keyword(s):  

Let [Formula: see text] [Formula: see text] be a perfect [Formula: see text]-manifold, [Formula: see text] be a component of [Formula: see text], [Formula: see text] be a homeomorphic map, [Formula: see text] and [Formula: see text]. In this paper, we show that if [Formula: see text] [Formula: see text] and [Formula: see text], then [Formula: see text]. As a corollary, if [Formula: see text] [Formula: see text] is a component of [Formula: see text], [Formula: see text] is a homeomorphic map, [Formula: see text], [Formula: see text], [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text], then [Formula: see text].


Author(s):  
David Bachman ◽  
Ryan Derby-Talbot ◽  
Eric Sedgwick
Keyword(s):  
Np Hard ◽  

2015 ◽  
Vol 22 (6) ◽  
pp. 1679-1698 ◽  
Author(s):  
Nathan M. Dunfield ◽  
Neil R. Hoffman ◽  
Joan E. Licata
Keyword(s):  

2014 ◽  
Vol 36 (1) ◽  
pp. 51-56
Author(s):  
Qilong Guo ◽  
Ruifeng Qiu ◽  
Yanqing Zou
Keyword(s):  

2014 ◽  
Vol 367 (8) ◽  
pp. 5753-5830 ◽  
Author(s):  
Kenneth L. Baker ◽  
Cameron Gordon ◽  
John Luecke

2014 ◽  
Vol 23 (09) ◽  
pp. 1450048 ◽  
Author(s):  
Paolo Aceto

We study the ribbon disks that arise from a symmetric union presentation of a ribbon knot. A natural notion of symmetric ribbon number rS(K) is introduced and compared with the classical ribbon number r(K). We show that the difference rS(K) - r(K) can be arbitrarily large by constructing an infinite family of ribbon knots Kn such that r(Kn) = 2 and rS(Kn) > n. The proof is based on a particularly simple description of symmetric unions in terms of certain band diagrams which leads to an upper bound for the Heegaard genus of their branched double covers.


Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Alberto Cavicchioli ◽  
Fulvia Spaggiari ◽  
Agnese Ilaria Telloni

We study a family of closed connected orientable 3-manifolds obtained by Dehn surgeries with rational coefficients along the oriented components of certain links. This family contains all the manifolds obtained by surgery along the (hyperbolic) 2-bridge knots. We find geometric presentations for the fundamental group of such manifolds and represent them as branched covering spaces. As a consequence, we prove that the surgery manifolds, arising from the hyperbolic 2-bridge knots, have Heegaard genus 2 and are 2-fold coverings of the 3-sphere branched over well-specified links.


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