The state-sum invariants for virtual knots
A.A.Kazakov
TL;DR
This paper introduces new non-trivial state-sum invariants for virtual knots and links, extending classical knot invariants through cohomology quandle theory and diagram colorings.
Contribution
It generalizes the Carter--Saito--Jelsovsky--Kamada--Langford theorem to virtual knots, providing a novel approach using cohomology quandle theory.
Findings
New non-trivial invariants for virtual knots and links
Extension of classical knot invariants to virtual knots
Use of cohomology quandle theory for diagram colorings
Abstract
We construct the new non-trivial state--sum invariants for virtual knots and links by a generalization of the powerful Carter--Saito--Jelsovsky--Kamada--Langford theorem for classical knots. The main result of this work is based on cohomology quandle theory and colorings of virtual knot and link diagrams by quandle elements.
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Taxonomy
TopicsGeometric and Algebraic Topology · Topological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology