36 citations · 177 across the 35 of their papers we have counts for
10 papers · 1 filter
A Proof of the Invariant Based Formula for the Linking Number and its Asymptotic Behaviour
Matt Bright, Olga Anosova, Vitaliy Kurlin
In 1833 Gauss defined the linking number of two disjoint curves in 3-space. For open curves this double integral over the parameterised curves is real-valued and invariant modulo r…
Encoding and Topological Computation on Textiles
Matt Bright, Vitaliy Kurlin
A textile structure is a periodic arrangement of threads in the thickened plane. A topological classification of textile structures is harder than for classical knots and links tha…
Computing braid groups of graphs with applications to robot motion planning
V. Kurlin
We design an algorithm writing down presentations of graph braid groups. Generators are represented in terms of actual motions of robots moving without collisions on a given graph.…
Recognizing trace graphs of closed braids
T. Fiedler, V. Kurlin
To a closed braid in a solid torus we associate a trace graph in a thickened torus in such a way that closed braids are isotopic if and only if their trace graphs can be related by…
All 2-dimensional links in 4-space live inside a universal 3-dimensional polyhedron
Cherry Kearton, Vitaliy Kurlin
The hexabasic book is the cone of the 1-dimensional skeleton of the union of two tetrahedra glued along a common face. The universal 3-dimensional polyhedron UP is the product of a…
Gauss paragraphs of classical links and a characterization of virtual link groups
V. Kurlin
A classical link in 3-space can be represented by a Gauss paragraph encoding a link diagram in a combinatorial way. A Gauss paragraph may code not a classical link diagram, but a d…
A 1-parameter approach to links in a solid torus
T. Fiedler, V. Kurlin
To an oriented link in a solid torus we associate a trace graph in a thickened torus in such a way that links are isotopic if and only if their trace graphs can be related by moves…
Peripherally specified homomorphs of link groups
V. Kurlin, D. Lines
Johnson and Livingston have characterized peripheral structures in homomorphs of knot groups. We extend their approach to the case of links. The main result is an algebraic charact…
Three-page encoding and complexity theory for spatial graphs
V. Kurlin
We construct a series of finitely presented semigroups. The centers of these semigroups encode uniquely up to rigid ambient isotopy in 3-space all non-oriented spatial graphs. This…
Three-page embeddings of singular knots
V. Kurlin, V. Vershinin
Construction of a semigroup with 15 generators and 84 relations is given. The center of this semigroup is in one-to-one correspondence with the set of all isotopy classes of non-or…