Zobrazeno 1 - 10
of 222
pro vyhledávání: '"Lambropoulou, Sofia"'
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
Publikováno v:
Symmetry 2024, 16(8), 968
In this paper we define novel topological invariants of doubly periodic tangles (DP tangles). DP tangles are embeddings of curves in the thickened plane with translational symmetries in two independent directions. We first organize the components of
Externí odkaz:
http://arxiv.org/abs/2404.05092
Given a knot or link in the handlebody, $H_g$, of genus $g$ we prove that it can always be represented as the plat closure of a braid in $H_g$. We further establish the Hilden braid group for the handlebody, as a subgroup of the mixed braid group, wh
Externí odkaz:
http://arxiv.org/abs/2312.10781
Doubly periodic tangles, or \textit{DP tangles}, are embeddings of curves in the thickened plane that are periodically repeated in two directions. They are completely defined by their generating cells, the {\it flat motifs}, which can be chosen in in
Externí odkaz:
http://arxiv.org/abs/2310.00822
Given a knot or link in the form of plat closure of a braid, we describe an algorithm to obtain a braid representing the same knot or link with the standard closure, and vice-versa. We analyze the three cases of knots and links: in \(\mathbb{R}^3\),
Externí odkaz:
http://arxiv.org/abs/2308.07291
To each rail knotoid we associate two unoriented knots along with their oriented counterparts, thus deriving invariants for rail knotoids based on these associations. We then translate them to invariants of rail isotopy for rail arcs.
Comment: 9
Comment: 9
Externí odkaz:
http://arxiv.org/abs/2111.02070
We extend the theory of Vassiliev (or finite type) invariants for knots to knotoids using two different approaches. Firstly, we take closures on knotoids to obtain knots and we use the Vassiliev invariants for knots, proving that these are knotoid is
Externí odkaz:
http://arxiv.org/abs/2010.01692
Autor:
Gügümcü, Neslihan, Lambropoulou, Sofia
Braidoids generalize the classical braids and form a counterpart theory to the theory of planar knotoids, just as the theory of braids does for the theory of knots. In this paper, we introduce basic notions of braidoids, a closure operation for braid
Externí odkaz:
http://arxiv.org/abs/1908.06053
The Jones polynomial is a famous link invariant that can be defined diagrammatically via a skein relation. Khovanov homology is a richer link invariant that categorifies the Jones polynomial. Using spectral sequences, we obtain a skein-type relation
Externí odkaz:
http://arxiv.org/abs/1904.07794
We work on the notions of rail arcs and rail isotopy in $\mathbb{R}^3$, and we introduce the notions of rail knotoid diagrams and their equivalence. Our main result is that two rail arcs in $\mathbb{R}^3$ are rail isotopic if and only if their knotoi
Externí odkaz:
http://arxiv.org/abs/1812.09493