Surface-link families with arbitrarily large triple point number

DOI10.1016/j.topol.2022.108234zbMath1500.57017arXiv2204.13860OpenAlexW4293211588WikidataQ114127830 ScholiaQ114127830MaRDI QIDQ2172646

Nicholas Cazet

Publication date: 16 September 2022

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.13860

zbMATH Keywords

surface-linktriple point numbersymmetric quandle cocycle invariant

Mathematics Subject Classification ID

Knot theory (57K10) Higher-dimensional knots and links (57K45)

Cites Work

• The length of a 3-cocycle of the 5-dihedral quandle
• Triple point numbers of surface-links and symmetric quandle cocycle invariants
• An estimate of the triple point numbers of surface-knots by quandle cocycle invariants
• Surfaces in 4-space
• Symmetric extensions of dihedral quandles and triple points of non-orientable surfaces
• No 2-knot has triple point number two or three
• Surface-Knots in 4-Space
• Homology groups of symmetric quandles and cocycle invariants of links and surface-links
• Computations of quandle cocycle invariants of surface-links using marked graph diagrams
• The 2-twist-spun trefoil has the triple point number four
• On non-orientable surfaces in 4-space which are projected with at most one triple point
• No surface-knot of genus one has triple point number two
• Non-additivity for triple point numbers on the connected sum of surface-knots
• Minimal triple point numbers of some non-orientable surface-links.
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