Zobrazeno 1 - 10
of 320
pro vyhledávání: '"57M27, 57M25"'
Howards and Kobin give a sharp upper bound for crossing number of knots on rectangular mosaics. Here we extend the proof to create a new bound for hexagonal mosaics in all three natural settings and shorten the proof in the rectangular setting.
Externí odkaz:
http://arxiv.org/abs/2410.19570
Autor:
Popović, David
We study algebraic obstructions to realizability of local equivalence classes of knot-like complexes. We classify local equivalence classes of knot-like complexes over $\mathbb{F}[U,V]$, answering a question of Dai, Hom, Stoffregen and Truong.
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Externí odkaz:
http://arxiv.org/abs/2306.04861
Autor:
Kotorii, Yuka, Mizusawa, Atsuhiko
Habegger and Lin gave a classification of the link-hmotopy classes of links as the link-homotopy classes of string links modulo the actions of conjugations and partial conjugations for string links. In this paper, we calculated the actions of the par
Externí odkaz:
http://arxiv.org/abs/2212.14502
Autor:
Ham, Ji-Young, Lee, Joongul
An explicit formula for the $A$-polynomial of the knot having Conway's notation $C(2n,4)$ is computed up to repeated factors. Our polynomial contains exactly the same irreducible factors as the $A$-polynomial defined in~\cite{CCGLS1}.
Comment: 1
Comment: 1
Externí odkaz:
http://arxiv.org/abs/2212.12985
Autor:
Kawagoe, Kenichi
We give a rigorous proof of the colored HOMFLY-PT polynomials of the trefoil knot, the figure-eight knot and twist knots. For the trefoil knot and the figure-eight knot, it is expressed by a single sum, and for a twist knot, it is expressed by a doub
Externí odkaz:
http://arxiv.org/abs/2107.08678
In the present paper we study structural aspects of certain quotients of braid groups and virtual braid groups. In particular, we construct and study linear representations $B_n\to {\rm GL}_{n(n-1)/2}\left(\mathbb{Z}[t^{\pm1}]\right)$, $VB_n\to {\rm
Externí odkaz:
http://arxiv.org/abs/2107.03875
Autor:
Diamantis, Ioannis
Publikováno v:
Communications in Mathematics, Volume 31 (2023), Issue 1 (December 13, 2022) cm:10438
In this paper we introduce and study the theories of pseudo links and singular links in the Solid Torus, ST. Pseudo links are links with some missing crossing information that naturally generalize the notion of knot diagrams, and that have potential
Externí odkaz:
http://arxiv.org/abs/2101.03538
Autor:
Meyer, Bradley, Tran, Anh T.
We compute the nonabelian $\mathrm{SL_2}(\mathbb{C})$-character varieties of the rational knots $C(2n+1,2m,2)$ in the Conway notation, where $m$ and $n$ are non-zero integers. By studying real points on these varieties, we determine the left orderabi
Externí odkaz:
http://arxiv.org/abs/2011.11623
Autor:
Khan, Arafat, Tran, Anh T.
We consider the classical pretzel knots $P(a_1, a_2, a_3)$, where $a_1, a_2, a_3$ are positive odd integers. By using continuous paths of elliptic $\mathrm{SL}_2(\mathbb R)$-representations, we show that (i) the 3-manifold obtained by $\frac{m}{l}$-s
Externí odkaz:
http://arxiv.org/abs/2011.08668
Autor:
Diamantis, Ioannis
In this paper we study the theory of {\it pseudo knots}, which are knots with some missing crossing information, and we introduce and study the theory of {\it pseudo tied links} and the theory of {\it pseudo knotoids}. In particular, we first present
Externí odkaz:
http://arxiv.org/abs/2010.06162