An estimate of the triple point numbers of surface-knots by quandle cocycle invariants

DOI10.1016/j.topol.2003.09.006zbMath1052.57031OpenAlexW1986694022MaRDI QIDQ1877605

Eri Hatakenaka

Publication date: 19 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.topol.2003.09.006

zbMATH Keywords

triple point numbersurface knotsquandle cocyle invariants

Mathematics Subject Classification ID

Embeddings and immersions in PL-topology (57Q35)

Related Items

Inequivalent surface-knots with the same knot quandle ⋮ No surface-knot of genus one has triple point number two ⋮ Surface-link families with arbitrarily large triple point number ⋮ Triple linking numbers and triple point numbers of certain \(T^2\)-links ⋮ The lower bound of the 𝑤-indices of surface links via quandle cocycle invariants ⋮ Triple point numbers of surface-links and symmetric quandle cocycle invariants ⋮ Symmetric extensions of dihedral quandles and triple points of non-orientable surfaces ⋮ ON SURFACE-LINKS REPRESENTED BY DIAGRAMS WITH TWO OR THREE TRIPLE POINTS ⋮ POLYNOMIAL COCYCLES OF ALEXANDER QUANDLES AND APPLICATIONS ⋮ THE ALGEBRA OF RACK AND QUANDLE COHOMOLOGY ⋮ ON TRIPLE POINT NUMBERS OF 5-COLORABLE 2-KNOTS

Cites Work

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• On simply knotted spheres in \(R^ 4\)
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• The 2-twist-spun trefoil has the triple point number four
• State-sum invariants of knotted curves and surfaces from quandle cohomology
• On non-orientable surfaces in 4-space which are projected with at most one triple point
• Alexander numbering of knotted surface diagrams
• AN INFINITE FAMILY OF NON-INVERTIBLE SURFACES IN 4-SPACE