Triple point numbers of surface-links and symmetric quandle cocycle invariants. (English) Zbl 1188.57017

Oshiro, Kanako

Algebr. Geom. Topol. 10, No. 2, 853-865 (2010).

Summary: For any positive integer \(n\), we give a 2-component surface-link \(F = F_1 \cup F_2\) such that \(F_1\) is orientable, \(F_2\) is non-orientable and the triple point number of \(F\) is equal to \(2n\). To give lower bounds of the triple point numbers, we use symmetric quandle cocycle invariants.

MSC:

57Q45	Knots and links in high dimensions (PL-topology) (MSC2010)
18G99	Homological algebra in category theory, derived categories and functors
55N99	Homology and cohomology theories in algebraic topology
57Q35	Embeddings and immersions in PL-topology

Keywords:

non-orientable surfaces; surface-links; symmetric quandles; triple point numbers

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