Dehn surgeries on some classical links

2011 ◽  
Vol 54 (1) ◽  
pp. 33-45 ◽  
Author(s):  
Alberto Cavicchioli ◽  
Fulvia Spaggiari ◽  
Agnese Ilaria Telloni
Keyword(s):  
Dehn Surgery ◽  
Fundamental Groups ◽  
Branched Coverings ◽  
Borromean Rings

AbstractWe consider orientable closed connected 3-manifolds obtained by performing Dehn surgery on the components of some classical links such as Borromean rings and twisted Whitehead links. We find geometric presentations of their fundamental groups and describe many of them as 2-fold branched coverings of the 3-sphere. Finally, we obtain some topological applications on the manifolds given by exceptional surgeries on hyperbolic 2-bridge knots.

scholarly journals On the cyclic coverings of the knot 52

1999 ◽  
Vol 42 (3) ◽  
pp. 575-587 ◽  
Author(s):  
P. Bandieri ◽  
A. C. Kim ◽  
M. Mulazzani
Keyword(s):  
Fundamental Groups ◽  
Branched Coverings ◽  
Homology Groups ◽  
Cyclic Coverings

We construct a family of hyperbolic 3-manifolds whose fundamental groups admit a cyclic presentation. We prove that all these manifolds are cyclic branched coverings of S3 over the knot 52 and we compute their homology groups. Moreover, we show that thecyclic presentations correspond to spines of the manifolds.

scholarly journals ON BRANCHED COVERINGS OF LENS SPACES

2004 ◽  
Vol 47 (2) ◽  
pp. 271-288 ◽  
Author(s):  
Elena Barbieri ◽  
Fulvia Spaggiari
Keyword(s):  
Subject Classification ◽  
Lens Spaces ◽  
Fundamental Groups ◽  
Branched Coverings ◽  
Covering Properties

AbstractWe construct some series of polyhedral schemata which represent orientable closed connected 3-manifolds. We show that these manifolds have spines corresponding to certain balanced presentations of their fundamental groups. Then we study some covering properties of such manifolds and prove that many of them are cyclic branched coverings of lens spaces. Our theorems contain a number of published results from various sources as particular cases.AMS 2000 Mathematics subject classification: Primary 57M12; 57M50; 57M60

scholarly journals A NOTE ON LENS SPACE SURGERIES: ORDERS OF FUNDAMENTAL GROUPS VERSUS SEIFERT GENERA

2011 ◽  
Vol 20 (04) ◽  
pp. 617-624 ◽  
Author(s):  
TOSHIO SAITO
Keyword(s):  
Fundamental Group ◽  
Lens Space ◽  
Dehn Surgery ◽  
Fundamental Groups

Let K be a non-trivial knot in the 3-sphere with a lens space surgery and L(p, q) a lens space obtained by a Dehn surgery on K. We study a relationship between the order p of the fundamental group of L(p, q) and the Seifert genus g of K. Considering certain infinite families of knots with lens space surgeries, the following estimation is suggested as a conjecture: [Formula: see text] except for (g, p) = (5, 19).

On the Cyclic Branched Coverings of the 2-Bridge Knot b(17,4)

2006 ◽  
Vol 13 (01) ◽  
pp. 173-180 ◽  
Author(s):  
Kwang-Woo Jeong
Keyword(s):  
Infinite Family ◽  
Fundamental Groups ◽  
Branched Coverings ◽  
Group Presentations

We construct an infinite family of hyperbolic 3-manifolds whose fundamental groups are cyclically presented. We prove that these 3-manifolds are cyclic branched coverings of S3over the 2-bridge knot b(17,4). Finally, we compute thehomology groups and discuss the spines of our manifolds which correspond to some group presentations.

scholarly journals Cyclic Branched Coverings Over Some Classes of (1,1)-Knots

Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Agnese Ilaria Telloni
Keyword(s):  
Parametric Family ◽  
Fundamental Groups ◽  
Split Extension ◽  
Torus Knots ◽  
Branched Coverings ◽  
Cyclic Coverings

We construct a 4-parametric family of combinatorial closed 3-manifolds, obtained by glueing together in pairs the boundary faces of polyhedral 3-balls. Then, we obtain geometric presentations of the fundamental groups of these manifolds and determine the corresponding split extension groups. Finally, we prove that the considered manifolds are cyclic coverings of the 3-sphere branched over well-specified -knots, including torus knots and Montesinos knots.

scholarly journals Left-Orderable Fundamental Groups and Dehn Surgery

2012 ◽  
Vol 2013 (12) ◽  
pp. 2862-2890 ◽  
Author(s):  
Adam Clay ◽  
Liam Watson
Keyword(s):  
Dehn Surgery ◽  
Fundamental Groups

scholarly journals About some infinite family of 2-bridge knots and3-manifolds

2000 ◽  
Vol 24 (2) ◽  
pp. 95-108 ◽  
Author(s):  
Yangkok Kim
Keyword(s):  
Infinite Family ◽  
Fundamental Groups ◽  
Branched Coverings

We construct an infinite family of 3-manifolds and show that these manifolds have cyclically presented fundamental groups and are cyclic branched coverings of the 3-sphere branched over the 2-bridge knots(ℓ+1)2or(ℓ+1)1, that are the closure of the rational(2ℓ−1)/(ℓ−1)-tangles or(2ℓ−1)/ℓ-tangles, respectively.

scholarly journals Left-orderable fundamental groups and Dehn surgery on genus one 2–bridge knots

2014 ◽  
Vol 14 (4) ◽  
pp. 2125-2148 ◽  
Author(s):  
Ryoto Hakamata ◽  
Masakazu Teragaito
Keyword(s):  
Dehn Surgery ◽  
Fundamental Groups ◽  
Genus One

Filling words in fundamental groups of Riemann surfaces

2013 ◽  
Vol 50 (1) ◽  
pp. 31-50
Author(s):  
C. Zhang
Keyword(s):  
Riemann Surface ◽  
Fundamental Group ◽  
Riemann Surfaces ◽  
Fundamental Groups ◽  
Closed Geodesics ◽  
New Words

The purpose of this article is to utilize some exiting words in the fundamental group of a Riemann surface to acquire new words that are represented by filling closed geodesics.

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