An invariant of graph-links valued in graphs and an almost classification of graph-links

DOI10.1142/S0218216520500637zbMath1457.57013OpenAlexW3037207538MaRDI QIDQ5131491

Vassily O. Manturov, D. P. Il'yutko

Publication date: 8 November 2020

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218216520500637

zbMATH Keywords

classificationinvariantminimalitygraph-linkfree knot

Mathematics Subject Classification ID

Relations of low-dimensional topology with graph theory (57M15) Associative rings and algebras arising under various constructions (16S99) Generalized knots (virtual knots, welded knots, quandles, etc.) (57K12)

Cites Work

• Unnamed Item
• An almost classification of free knots
• Chords in a circle and linear algebra over GF(2)
• Graph-links
• Cycle decomposition by disjoint transpositions
• Circle graph obstructions
• A graphical construction of the sl(3) invariant for virtual knots
• FIBERED KNOTS AND VIRTUAL KNOTS
• GRAPH-VALUED INVARIANTS OF VIRTUAL AND CLASSICAL LINKS AND MINIMALITY PROBLEM
• AN EQUIVALENCE BETWEEN THE SET OF GRAPH-KNOTS AND THE SET OF HOMOTOPY CLASSES OF LOOPED GRAPHS
• A BRACKET POLYNOMIAL FOR GRAPHS, IV: UNDIRECTED EULER CIRCUITS, GRAPH-LINKS AND MULTIPLY MARKED GRAPHS
• INTRODUCTION TO GRAPH-LINK THEORY
• FREE KNOTS AND GROUPS
• THE QUANTUM G₂ LINK INVARIANT
• VASSILIEV KNOT INVARIANTS COMING FROM LIE ALGEBRAS AND 4-INVARIANTS
• Khovanov homology of graph-links
• Parity in knot theory