Crossing distances of surface-knots

Tsukasa Yashiro*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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
Issue number7 SPEC. ISS.
Publication statusPublished - Apr 1 2007


  • Distance
  • Surface-knot
  • Trivial surface

ASJC Scopus subject areas

  • Geometry and Topology


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