Tuesday Seminar on Topology

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Date, time & place	Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.)
Organizer(s)	HABIRO Kazuo, KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya

2012/05/29

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Inasa Nakamura (Gakushuin University, JSPS)
Triple linking numbers and triple point numbers
of torus-covering

$T^2$ -links
(JAPANESE)

[ Abstract ]
The triple linking number of an oriented surface link was defined as an
analogical notion of the linking number of a classical link. A
torus-covering

$T^2$ -link

$\\mathcal{S}_m(a,b)$ is a surface link in the
form of an unbranched covering over the standard torus, determined from
two commutative

$m$ -braids

$a$ and

$b$ .
In this talk, we consider

$\\mathcal{S}_m(a,b)$ when

$a$ ,

$b$ are pure

$m$ -braids (

$m \\geq 3$ ), which is a surface link with

$m$ -components. We
present the triple linking number of

$\\mathcal{S}_m(a,b)$ 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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