Tuesday Seminar on Topology

Research Graduate program Undergraduate education

Activities

Visitor information

Seminar information archive ～06/23｜Next seminar｜Future seminars 06/24～

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

2011/01/25

16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Chikara Haruta (Graduate School of Mathematical Sciences, the University of Tokyo )
On unknotting of surface-knots with small sheet numbers
(JAPANESE)

[ Abstract ]
A connected surface smoothly embedded in

${\\mathbb R}^4$ is called a surface-knot. In particular, if a surface-knot

$F$ is homeomorphic to the

$2$ -sphere or the torus, then it is called an

$S^2$ -knot or a

$T^2$ -knot, respectively. The sheet number of a surface-knot is an invariant analogous to the crossing number of a

$1$ -knot. M. Saito and S. Satoh proved some results concerning the sheet number of an

$S^2$ -knot. In particular, it is known that an

$S^2$ -knot is trivial if and only if its sheet number is

$1$ , and there is no

$S^2$ -knot whose sheet number is

$2$ . In this talk, we show that there is no

$S^2$ -knot whose sheet number is

$3$ , and a

$T^2$ -knot is trivial if and only if its sheet number is

$1$ .

Graduate School of Mathematical Sciences, The University of Tokyo

3-8-1 Komaba Meguro-ku Tokyo 153-8914, Japan TEL: 03-5465-7001 FAX: 03-5465-7011