Sliceness of alternating pretzel knots and links

2020 ◽  
Vol 282 ◽  
pp. 107317
Author(s):  
Kengo Kishimoto ◽  
Tetsuo Shibuya ◽  
Tatsuya Tsukamoto
Keyword(s):  
Pretzel Knots ◽  
Knots And Links

scholarly journals Colored HOMFLY polynomials for the pretzel knots and links

2015 ◽  
Vol 2015 (7) ◽  
Author(s):  
A. Mironov ◽  
A. Morozov ◽  
A. Sleptsov
Keyword(s):  
Pretzel Knots ◽  
Homfly Polynomials ◽  
Knots And Links

Identifying non-pseudo-alternating knots by using the free factor property of minimal genus Seifert surfaces

2021 ◽  
Author(s):  
Keisuke Himeno ◽  
Masakazu Teragaito
Keyword(s):  
Seifert Surface ◽  
Major Difficulty ◽  
Flat Surfaces ◽  
Minimal Genus ◽  
Pretzel Knots ◽  
Seifert Surfaces ◽  
Manifold Theory ◽  
Knots And Links

Pseudo-alternating knots and links are defined constructively via their Seifert surfaces. By performing Murasugi sums of primitive flat surfaces, such a knot or link is obtained as the boundary of the resulting surface. Conversely, it is hard to determine whether a given knot or link is pseudo-alternating or not. A major difficulty is the lack of criteria to recognize whether a given Seifert surface is decomposable as a Murasugi sum. In this paper, we propose a new idea to identify non-pseudo-alternating knots. Combining with the uniqueness of minimal genus Seifert surface obtained through sutured manifold theory, we demonstrate that two infinite classes of pretzel knots are not pseudo-alternating.

scholarly journals Colored knot polynomials for arbitrary pretzel knots and links

2015 ◽  
Vol 743 ◽  
pp. 71-74 ◽  
Author(s):  
D. Galakhov ◽  
D. Melnikov ◽  
A. Mironov ◽  
A. Morozov ◽  
A. Sleptsov
Keyword(s):  
Pretzel Knots ◽  
Knots And Links

The Lehmer Polynomial and Pretzel Links

2001 ◽  
Vol 44 (4) ◽  
pp. 440-451 ◽  
Author(s):  
Eriko Hironaka
Keyword(s):  
Alexander Polynomial ◽  
Mahler Measure ◽  
Integer Polynomials ◽  
Pretzel Knots ◽  
Positive Integers ◽  
Knots And Links

AbstractIn this paper we find a formula for the Alexander polynomial Δp1,…,pk (x) of pretzel knots and links with (p1,…,pk,−1) twists, where k is odd and p1,…, pk are positive integers. The polynomial Δ2,3,7(x) is the well-known Lehmer polynomial, which is conjectured to have the smallest Mahler measure among all monic integer polynomials. We confirm that Δ2,3,7(x) has the smallest Mahler measure among the polynomials arising as Δp1,…,pk (x).

scholarly journals The rational Khovanov homology of 3-strand pretzel links

2014 ◽  
Vol 23 (08) ◽  
pp. 1450040 ◽  
Author(s):  
Andrew Manion
Keyword(s):  
General Formula ◽  
Knot Theory ◽  
Rational Numbers ◽  
Khovanov Homology ◽  
Pretzel Knots ◽  
Knots And Links

The 3-strand pretzel knots and links are a well-studied source of examples in knot theory. However, while there have been computations of the Khovanov homology and Rasmussen s-invariants of some sub-families of 3-strand pretzel knots, no general formula has been given for all of them. We give a formula for the unreduced Khovanov homology, over the rational numbers, of all 3-strand pretzel links. We also compute generalized s-invariants of these links.

Knots and Links

2004 ◽  
Author(s):  
Peter R. Cromwell
Keyword(s):  
Knots And Links

scholarly journals Invariants of Random Knots and Links

2016 ◽  
Vol 56 (2) ◽  
pp. 274-314 ◽  
Author(s):  
Chaim Even-Zohar ◽  
Joel Hass ◽  
Nati Linial ◽  
Tahl Nowik
Keyword(s):  
Knots And Links ◽  
Random Knots

DELTA-UNKNOTTING NUMBER FOR KNOTS

1998 ◽  
Vol 07 (05) ◽  
pp. 639-650 ◽  
Author(s):  
K. NAKAMURA ◽  
Y. NAKANISHI ◽  
Y. UCHIDA
Keyword(s):  
Torus Knots ◽  
Pretzel Knots ◽  
Minimum Number

The Δ-unknotting number for a knot is defined to be the minimum number of Δ-unknotting operations which deform the knot into the trivial knot. We determine the Δ-unknotting numbers for torus knots, positive pretzel knots, and positive closed 3-braids.

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