### Abstract

A surface-knot is an embedded closed connected oriented surface in 4-space. A surface diagram is a projection of a surface-knot into 3-space with crossing information. In this paper we define a distance from a special surface diagram to a trivial diagram as the minimal number of special double cycles, where we can change the crossing information to obtain the trivial diagram. We estimate the distance using the number of 1-handles needed to obtain a trivial diagram.

Original language | English |
---|---|

Pages (from-to) | 1532-1539 |

Number of pages | 8 |

Journal | Topology and its Applications |

Volume | 154 |

Issue number | 7 SPEC. ISS. |

DOIs | |

Publication status | Published - Apr 1 2007 |

### Fingerprint

### Keywords

- Distance
- Surface-knot
- Trivial surface

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Topology and its Applications*,

*154*(7 SPEC. ISS.), 1532-1539. https://doi.org/10.1016/j.topol.2006.04.028

**Crossing distances of surface-knots.** / Yashiro, Tsukasa.

Research output: Contribution to journal › Article

*Topology and its Applications*, vol. 154, no. 7 SPEC. ISS., pp. 1532-1539. https://doi.org/10.1016/j.topol.2006.04.028

}

TY - JOUR

T1 - Crossing distances of surface-knots

AU - Yashiro, Tsukasa

PY - 2007/4/1

Y1 - 2007/4/1

N2 - A surface-knot is an embedded closed connected oriented surface in 4-space. A surface diagram is a projection of a surface-knot into 3-space with crossing information. In this paper we define a distance from a special surface diagram to a trivial diagram as the minimal number of special double cycles, where we can change the crossing information to obtain the trivial diagram. We estimate the distance using the number of 1-handles needed to obtain a trivial diagram.

AB - A surface-knot is an embedded closed connected oriented surface in 4-space. A surface diagram is a projection of a surface-knot into 3-space with crossing information. In this paper we define a distance from a special surface diagram to a trivial diagram as the minimal number of special double cycles, where we can change the crossing information to obtain the trivial diagram. We estimate the distance using the number of 1-handles needed to obtain a trivial diagram.

KW - Distance

KW - Surface-knot

KW - Trivial surface

UR - http://www.scopus.com/inward/record.url?scp=33947107520&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33947107520&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2006.04.028

DO - 10.1016/j.topol.2006.04.028

M3 - Article

VL - 154

SP - 1532

EP - 1539

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 7 SPEC. ISS.

ER -