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6 papers · 1 filter
On Virtual Crossing Number Estimates For Virtual Links
Denis Afanasiev, Vassily Manturov
We address the question of detecting minimal virtual diagrams with respect to the number of virtual crossings. This problem is closely connected to the problem of detecting the min…
Introduction to Graph-Link Theory
Denis P. Ilyutko, Vassily O. Manturov
The present paper is an introduction to a combinatorial theory arising as a natural generalisation of classical and virtual knot theory. There is a way to encode links by a class o…
Homotopy type of the complement of an immersion and classification of embeddings of tori
M. Cencelj, D. Repovš, M. Skopenkov
This paper is devoted to the classification of embeddings of higher dimensional manifolds. We study the case of embeddings , which we call knotted tori. The s…
The Khovanov Complex for Virtual Links
Vassily Olegovich Manturov
In the present paper, we construct the Khovanov homology theory for virtual links. Besides the direct approach with Z_{2} coefficients we also describe the Khovanov homology for fr…
Energy of a knot: variational principles; Mm-energy
O. N. Karpenkov
Let be the energy of some knot for any from certain class of functions. The problem is to find knots with extremal values of energy. We discuss the notion of the loca…
Virtual Knot Theory --Unsolved Problems
Roger Fenn, Louis H. Kauffman, Vassily O. Manturov
This paper is an introduction to the theory of virtual knots and links and it gives a list of unsolved problems in this subject.