Zobrazeno 1 - 10
of 489
pro vyhledávání: '"57K12"'
Autor:
Sekino, Nozomu
Flat virtual links are some variant of links, and semiquandles are counterparts of quandles or biquandles, which axiomize the Reidemeister-like moves. In this paper, we give some example of semiquandle and introduce an invariant for flat virtual knot
Externí odkaz:
http://arxiv.org/abs/2411.04725
Autor:
Nelson, Sam
We define a family of quiver representation-valued invariants of oriented classical and virtual knots and links associated to a choice of finite quandle $X$, abelian group $A$, set of quandle 2-cocycles $C\subset H^2_Q(x;A)$, choice of coefficient ri
Externí odkaz:
http://arxiv.org/abs/2411.02153
Autor:
Jibiki, Chihaya
We construct a continuous map from the space of orders on quandles to the space of quandle actions on one-manifolds, providing an answer to a question posed by Idrissa Ba and Mohamed Elhamdadi. As an application of this map, we characterize isolated
Externí odkaz:
http://arxiv.org/abs/2410.21476
Autor:
Panagiotou, Eleni
This manuscript introduces a new framework for the study of knots by exploring the neighborhood of knot embeddings in the space of simple open and closed curves in 3-space. The latter gives rise to a knotoid spectrum, which determines the knot type v
Externí odkaz:
http://arxiv.org/abs/2410.15593
We define twelve equivalence relations on $\mathbb{Z}^{m}$ ($m\geq2$) by means of Fox's $\mathbb{Z}$-colorings of (classical, virtual, or pure) $m$-braids and $(m,m)$-tangles. One of them corresponds to the Hurwitz action of the $m$-braid group on $\
Externí odkaz:
http://arxiv.org/abs/2410.11599
Autor:
Bardakov, V. G., Iskra, A. L.
The class transposition group $CT(\mathbb{Z})$ was introduced by S. Kohl in 2010. It is a countable subgroup of the permutation group $Sym(\mathbb{Z})$ of the set of integers $\mathbb{Z}$. We study products of two class transpositions $CT(\mathbb{Z})
Externí odkaz:
http://arxiv.org/abs/2409.13341
Autor:
Kauffman, Louis H
This paper discusses a generalization of virtual knot theory that we call multi-virtual knot theory. Multi-virtual knot theory uses a multiplicity of types of virtual crossings. As we will explain, this multiplicity is motivated by the way it arises
Externí odkaz:
http://arxiv.org/abs/2409.07499
In this paper, we extend the theory of planar pseudo knots to the theories of annular and toroidal pseudo knots. Pseudo knots are defined as equivalence classes under Reidemeister-like moves of knot diagrams characterized by crossings with undefined
Externí odkaz:
http://arxiv.org/abs/2409.03537
Autor:
Kindred, Thomas
Gabai proved that any plumbing, or Murasugi sum, of $\pi_1$-essential Seifert surfaces is also $\pi_1$-essential, and Ozawa extended this result to unoriented spanning surfaces. We show that the analogous statement about geometrically essential surfa
Externí odkaz:
http://arxiv.org/abs/2408.16948
We introduce a generalization of the quandle polynomial. We prove that our polynomial is an invariant of stuquandles. Furthermore, we use the invariant of stuquandles to define a polynomial invariant of stuck links. As a byproduct, we obtain a polyno
Externí odkaz:
http://arxiv.org/abs/2408.07695