7 papers · 1 filter
A table of knotoids in up to seven crossings
Boštjan Gabrovšek, Paolo Cavicchioli
We present a complete classification of spherical knotoids with up to six crossings and conjecture that our classification up to seven crossings is complete. Our work extends the t…
Bonded braids and the Markov theorem
Paolo Cavicchioli, Boštjan Gabrovšek, Matic Simonič
Bonded knots arise naturally in topological protein modeling, where intramolecular interactions such as disulfide bridges stabilize folded configurations. These structures extend c…
Knots and non-orientable surfaces in 3-manifolds
Alessia Cattabriga, Paolo Cavicchioli, Rama Mishra +1
In this article, we propose a new approach for describing and understanding knots and links in a 3-manifold through the use of an embedded non-orientable surface. Specifically, we…
The mixed Hilden braid group and the plat equivalence in handlebodies
Paolo Cavicchioli, Sofia Lambropoulou
Given a knot or link in the handlebody, , of genus we prove that it can always be represented as the plat closure of a braid in . We further establish the Hilden brai…
A Markov theorem for plat closure of surface braids in Dunwoody and periodic Takahashi manifolds
Alessia Cattabriga, Paolo Cavicchioli
In this article we deal with the problem of finding equivalence moves for links in Dunwoody and periodic Takahashi manifolds. We represent these manifolds using Heegaard splitting…
Passing from plat closure to standard closure of braids in , in handlebodies and in thickened surfaces
Paolo Cavicchioli, Sofia Lambropoulou
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…
An algorithmic method to compute plat-like Markov moves for genus two 3-manifolds
Paolo Cavicchioli
This article deals with equivalence of links in 3-manifolds of Heegaard genus 2. Starting from a description of such a manifold introduced by Casali et al., that uses 6-tuples of i…