The state-sum invariants for virtual knots

2018/09/16 by A. A. Kazakov, Kazakov, A. A.
Computer Science · Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1809.05871

openalex publication_date 2018/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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