## Tuesday Seminar on Topology

Seminar information archive ～05/18｜Next seminar｜Future seminars 05/19～

Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
---|---|

Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |

### 2013/12/17

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Satellites of an oriented surface link and their local moves (JAPANESE)

**Inasa Nakamura**(The University of Tokyo)Satellites of an oriented surface link and their local moves (JAPANESE)

[ Abstract ]

For an oriented surface link $F$ in $\\mathbb{R}^4$,

we consider a satellite construction of a surface link, called a

2-dimensional braid over $F$, which is in the form of a covering over

$F$. We introduce the notion of an $m$-chart on a surface diagram

$p(F)\\subset \\mathbb{R}^3$ of $F$, which is a finite graph on $p(F)$

satisfying certain conditions and is an extended notion of an

$m$-chart on a 2-disk presenting a surface braid.

A 2-dimensional braid over $F$ is presented by an $m$-chart on $p(F)$.

It is known that two surface links are equivalent if and only if their

surface diagrams are related by a finite sequence of ambient isotopies

of $\\mathbb{R}^3$ and local moves called Roseman moves.

We show that Roseman moves for surface diagrams with $m$-charts can be

well-defined. Further, we give some applications.

For an oriented surface link $F$ in $\\mathbb{R}^4$,

we consider a satellite construction of a surface link, called a

2-dimensional braid over $F$, which is in the form of a covering over

$F$. We introduce the notion of an $m$-chart on a surface diagram

$p(F)\\subset \\mathbb{R}^3$ of $F$, which is a finite graph on $p(F)$

satisfying certain conditions and is an extended notion of an

$m$-chart on a 2-disk presenting a surface braid.

A 2-dimensional braid over $F$ is presented by an $m$-chart on $p(F)$.

It is known that two surface links are equivalent if and only if their

surface diagrams are related by a finite sequence of ambient isotopies

of $\\mathbb{R}^3$ and local moves called Roseman moves.

We show that Roseman moves for surface diagrams with $m$-charts can be

well-defined. Further, we give some applications.