Triple linking numbers and triple point numbers of certain T2-links

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 T2-link (m⩾3) determined from two commutative pure m-braids a and b. We present the triple linking number of such a T2-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.