Crossing distances of surface-knots

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)1532-1539
Number of pages8
JournalTopology and its Applications
Volume154
Issue number7 SPEC. ISS.
DOIs
Publication statusPublished - Apr 1 2007

Fingerprint

Knot
Diagram
Trivial
Projection
Cycle
Closed
Estimate

Keywords

  • Distance
  • Surface-knot
  • Trivial surface

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

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

In: Topology and its Applications, Vol. 154, No. 7 SPEC. ISS., 01.04.2007, p. 1532-1539.

Research output: Contribution to journalArticle

Yashiro, Tsukasa. / Crossing distances of surface-knots. In: Topology and its Applications. 2007 ; Vol. 154, No. 7 SPEC. ISS. pp. 1532-1539.
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