Crossing distances of surface-knots

Tsukasa Yashiro

doi:10.1016/j.topol.2006.04.028

Crossing distances of surface-knots

Tsukasa Yashiro^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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	https://doi.org/10.1016/j.topol.2006.04.028
Publication status	Published - Apr 1 2007

Keywords

Distance
Surface-knot
Trivial surface

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2006.04.028

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title = "Crossing distances of surface-knots",

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.",

keywords = "Distance, Surface-knot, Trivial surface",

author = "Tsukasa Yashiro",

note = "Funding Information: The author is supported by JSPS post doctoral fellowship for foreign researchers. He would like to thank to Professor S. Kamada and Professor A. Kawauchi for giving him helpful suggestions for the early version of this paper.",

year = "2007",

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doi = "10.1016/j.topol.2006.04.028",

language = "English",

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TY - JOUR

T1 - Crossing distances of surface-knots

AU - Yashiro, Tsukasa

N1 - Funding Information: The author is supported by JSPS post doctoral fellowship for foreign researchers. He would like to thank to Professor S. Kamada and Professor A. Kawauchi for giving him helpful suggestions for the early version of this paper.

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

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U2 - 10.1016/j.topol.2006.04.028

DO - 10.1016/j.topol.2006.04.028

M3 - Article

AN - SCOPUS:33947107520

SN - 0166-8641

VL - 154

SP - 1532

EP - 1539

JO - Topology and its Applications

JF - Topology and its Applications

IS - 7 SPEC. ISS.

ER -

Crossing distances of surface-knots

Abstract

Keywords

ASJC Scopus subject areas

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