Mutant knots and intersection graphs

DOI10.2140/agt.2007.7.1579zbMath1158.57013arXiv0704.1313OpenAlexW2018050548MaRDI QIDQ2464924

Sergei K. Lando, Sergei Chmutov

Publication date: 18 December 2007

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0704.1313

zbMATH Keywords

intersection graphsVassiliev invariantsmutant knotsLie algebra weight systems

Mathematics Subject Classification ID

Related Items (20)

Values of the weight system on a family of graphs that are not the intersection graphs of chord diagrams ⋮ Values of the \(\mathfrak{sl}_2\) weight system on complete bipartite graphs ⋮ Partial-dual polynomials and signed intersection graphs ⋮ From matrix pivots to graphs in surfaces: exploring combinatorics through partial duals ⋮ A link surgery spectral sequence in monopole Floer homology ⋮ Values of the $\mathfrak{sl}_2$ weight system at chord diagrams with complete intersection graphs ⋮ New approaches to $\mathfrak{gl}_N$ weight system ⋮ Algebra of shares, complete bipartite graphs and $\mathfrak{sl}_2$ weight system ⋮ On the Lie superalgebra \(\mathfrak{gl}(m | n)\) weight system ⋮ Parity in knot theory and graph-links ⋮ The transition matroid of a 4-regular graph: an introduction ⋮ A 2-isomorphism theorem for delta-matroids ⋮ Criteria for the height of an atom ⋮ Homotopy type of circle graph complexes motivated by extreme Khovanov homology ⋮ On a weight system conjecturally related to \(\mathfrak{s}l_2\) ⋮ Embeddings of Four-valent Framed Graphs into 2-surfaces ⋮ Invariants of Graphs Modeling Nucleotide Rearrangements ⋮ An extension of the \(\mathfrak{sl}_2\) weight system to graphs with \(n \le 8\) vertices ⋮ A BRACKET POLYNOMIAL FOR GRAPHS, I ⋮ The space of framed chord diagrams as a Hopf module

Uses Software

• Knot Atlas

Cites Work

• Circle graphs and monadic second-order logic
• Reducing prime graphs and recognizing circle graphs
• Circle graph obstructions
• The universal Vassiliev invariant for the Lie superalgebra \(gl(1|1)\)
• Graphs on surfaces and their applications. Appendix by Don B. Zagier
• On the Vassiliev knot invariants
• On a Hopf algebra in graph theory
• Vassiliev knot invariants and Lie \(S\)-algebras
• Remarks on the Vassiliev knot invariants coming from \(sl_ 2\)
• Introduction to Vassiliev Knot Invariants
• INTERSECTION GRAPHS FOR STRING LINKS
• Decomposition of Directed Graphs
• Recognizing circle graphs in polynomial time
• DISTINGUISHING MUTANTS BY KNOT POLYNOMIALS
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Mutant knots and intersection graphs