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

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

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

scholarly journals COLORED HOMFLY POLYNOMIALS FROM CHERN–SIMONS THEORY

2013 ◽  
Vol 22 (13) ◽  
pp. 1350078 ◽  
Author(s):  
SATOSHI NAWATA ◽  
P. RAMADEVI ◽  
ZODINMAWIA
Keyword(s):  
Simons Theory ◽  
Theoretic Method ◽  
Two Component ◽  
6J Symbols ◽  
Multiplicity Free ◽  
Homfly Polynomials ◽  
Chern Simons ◽  
Knots And Links ◽  
Chern Simons Theory

We elaborate the Chern–Simons field theoretic method to obtain colored HOMFLY invariants of knots and links. Using multiplicity-free quantum 6j-symbols for Uq(𝔰𝔩N), we present explicit evaluations of the HOMFLY invariants colored by symmetric representations for a variety of knots, two-component links and three-component links.

scholarly journals Evolution method and HOMFLY polynomials for virtual knots

2015 ◽  
Vol 30 (14) ◽  
pp. 1550074 ◽  
Author(s):  
Ludmila Bishler ◽  
Alexei Morozov ◽  
Andrey Morozov ◽  
Anton Morozov
Keyword(s):  
Infinite Series ◽  
Symmetric Representation ◽  
Virtual Knots ◽  
Topological Invariance ◽  
Definition Of ◽  
Homfly Polynomials ◽  
Knots And Links

Following the suggestion of Alexei Morozov, Andrey Morozov and Anton Morozov, Phys. Lett. B737, 48 (2014), arXiv:1407.6319, to lift the knot polynomials for virtual knots and links from Jones to HOMFLY, we apply the evolution method to calculate them for an infinite series of twist-like virtual knots and antiparallel two-strand links. Within this family one can check topological invariance and understand how differential hierarchy is modified in virtual case. This opens a way towards a definition of colored (not only cabled) knot polynomials, though problems still persist beyond the first symmetric representation.

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).

EXPLICIT DESCRIPTION OF THE HOMFLY POLYNOMIALS FOR 2-BRIDGE KNOTS AND LINKS

2002 ◽  
Vol 11 (04) ◽  
pp. 565-574 ◽  
Author(s):  
SHIGEKAZU NAKABO
Keyword(s):  
Explicit Formula ◽  
Classification Problem ◽  
Explicit Description ◽  
Homfly Polynomial ◽  
Homfly Polynomials ◽  
Knots And Links

An explicit formula of the HOMFLY polynomial of 2-bridge knots and links is presented. As corollaries, some specific coefficient polynomials are described explicitly. Lastly, some examples are calculated, which are related to the classification problem of the 2-bridge knots and links by the HOMFLY polynomial.

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
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