scholarly journals Generalized crossing changes in satellite knots

2014 ◽  
Vol 143 (1) ◽  
pp. 447-458
Author(s):  
Cheryl Jaeger Balm
Keyword(s):  
Satellite Knots

scholarly journals On the Upsilon invariant and satellite knots

2018 ◽  
Vol 292 (3-4) ◽  
pp. 1431-1452
Author(s):  
Peter Feller ◽  
JungHwan Park ◽  
Arunima Ray
Keyword(s):  
Satellite Knots

The Neuwirth Conjecture for a family of satellite knots

2019 ◽  
Vol 28 (02) ◽  
pp. 1950017
Author(s):  
Mario Eudave-Muñoz ◽  
José Frías
Keyword(s):  
Closed Surface ◽  
Explicit Constructions ◽  
Satellite Knots

Let [Formula: see text] be a nontrivial knot in [Formula: see text]. It was conjectured that there exists a Neuwirth surface for [Formula: see text]. That is, a closed surface in [Formula: see text] containing the knot [Formula: see text] as a nonseparating curve and such that every compressing disk for the surface intersects the knot in at least two points. We provide explicit constructions of Neuwirth surfaces for a family of satellite knots, which do not depend on the existence of nonorientable algebraically incompressible and [Formula: see text]-incompressible spanning surfaces for these knots.

scholarly journals Cyclic surgery and satellite knots

1990 ◽  
Vol 36 (3) ◽  
pp. 205-208 ◽  
Author(s):  
Ying-Qing Wu
Keyword(s):  
Cyclic Surgery ◽  
Satellite Knots

scholarly journals $3$-manifolds with planar presentations and the width of satellite knots

2005 ◽  
Vol 358 (9) ◽  
pp. 3781-3805 ◽  
Author(s):  
Martin Scharlemann ◽  
Jennifer Schultens
Keyword(s):  
Satellite Knots

scholarly journals On Two Generator Satellite Knots

2004 ◽  
Vol 104 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Steven A. Bleiler ◽  
Amelia C. Jones
Keyword(s):  
Satellite Knots

scholarly journals Satellite knots and L-space surgeries

2016 ◽  
Vol 48 (5) ◽  
pp. 771-778 ◽  
Author(s):  
Jennifer Hom
Keyword(s):  
Satellite Knots

scholarly journals Tangle decompositions of satellite knots

1999 ◽  
Vol 12 (2) ◽  
Author(s):  
Hiroshi Matsuda ◽  
Makoto Ozawa ◽  
Chuichiro Hayashi
Keyword(s):  
Satellite Knots

FIBERED TORTI-RATIONAL KNOTS

2010 ◽  
Vol 19 (10) ◽  
pp. 1291-1353 ◽  
Author(s):  
MIKAMI HIRASAWA ◽  
KUNIO MURASUGI
Keyword(s):  
Arbitrary Number ◽  
Continued Fraction ◽  
Alexander Polynomials ◽  
Minimal Genus ◽  
Seifert Surfaces ◽  
Tunnel Number ◽  
Rational Knots ◽  
Geometric Techniques ◽  
Continued Fraction Expansions ◽  
Satellite Knots

A torti-rational knot, denoted by K(2α, β|r), is a knot obtained from the 2-bridge link B(2α, β) by applying Dehn twists an arbitrary number of times, r, along one component of B(2α, β). We determine the genus of K(2α, β|r) and solve a question of when K(2α, β|r) is fibered. In most cases, the Alexander polynomials determine the genus and fiberedness of these knots. We develop both algebraic and geometric techniques to describe the genus and fiberedness by means of continued fraction expansions of β/2α. Then, we explicitly construct minimal genus Seifert surfaces. As an application, we solve the same question for the satellite knots of tunnel number one.

On lassos and the Jones polynomial of satellite knots

2016 ◽  
Vol 25 (02) ◽  
pp. 1650011
Author(s):  
Adrián Jiménez Pascual
Keyword(s):  
Jones Polynomial ◽  
Solid Torus ◽  
Alexander Polynomial ◽  
New Family ◽  
Jones Polynomials ◽  
Polynomial Formula ◽  
Satellite Knots

In this paper, I present a new family of knots in the solid torus called lassos, and their properties. Given a knot [Formula: see text] with Alexander polynomial [Formula: see text], I then use these lassos as patterns to construct families of satellite knots that have Alexander polynomial [Formula: see text] where [Formula: see text]. In particular, I prove that if [Formula: see text] these satellite knots have different Jones polynomials.

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