Sharp-unknotting number and the Alexander module

Hitoshi Murakami, Sakuko Sakai

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

Suppose that a knot is deformed into another knot by a ν-unknotting operation. Then we will show that the difference of their Nakanishi indices is less than or equal to three and that the difference of the minimum numbers of generators of the first homology groups of their double branched covers is less than or equal to two. We also give infinitely many examples of composite knots with ν-unknotting number one.

Original languageEnglish
Pages (from-to)169-179
Number of pages11
JournalTopology and its Applications
Volume52
Issue number2
DOIs
Publication statusPublished - 1993 Oct 11

Keywords

  • Alexander module
  • Double branched cover
  • Knot
  • Nakanishi index
  • ν-unknotting number

ASJC Scopus subject areas

  • Geometry and Topology

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