Covering diagrams over surface-knot diagrams

Tsukasa Yashiro*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

A surface-knot is a closed oriented surface smoothly embedded in 4-space and a surface-knot diagram is a projected image of a surface-knot under the orthogonal projection in 3-space with crossing nformation. Every surface-knot diagram induces a rectangular-cell complex. In this paper, we introduce a covering diagram over a surface-knot diagram. the covering map induces a covering of the rectangular-cell complexes. As an application, a lower bound of triple point numbers for a family of surface-knots is obtained.

Original languageEnglish
Article number1850042
JournalJournal of Knot Theory and its Ramifications
Volume27
Issue number6
DOIs
Publication statusPublished - May 1 2018

Keywords

  • covering diagram
  • pseudo-cycle
  • Surface-knot
  • triple point

ASJC Scopus subject areas

  • Algebra and Number Theory

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