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

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

2011-02-18

arxiv.org/abs/1102.3736v2

Top. Appl. 159 (2012) 1439-1447

Mathematics

Geometric Topology

15 pages, 4 figures, minor modifications

Scientific paper

10.1016/j.topol.2012.01.004

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 ($m \geq 3$) 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.

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