Triple linking numbers and triple point numbers of certain $T^2$-links

Abstract

The triple linking number of an oriented surface link was defined as an analogical notion of the linking number of a classical link. We consider a certain $m$-component $T^2$-link ($m\ge 3$) determined from two commutative pure $m$-braids $a$ and $b$. We present the triple linking number of such a $T^2$-link, by using the linking numbers of the closures of $a$ and $b$. This gives a lower bound of the triple point number. In some cases, we can determine the triple point numbers, each of which is a multiple of four.

15 pages, 4 figures, minor modifications

References in corpus (1)

• Surface links which are coverings over the standard torus

Cited by in corpus (3)

• Surface links with free abelian link groups
• On surface links whose link groups are abelian
• Showing distinctness of surface links by taking 2-dimensional braids