A new aspect of the arnold invariant J+ from a global viewpoint

Kenta Hayano, Noboru Ito

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, we study the Arnold invariant J+ for plane and spherical curves. This invariant essentially counts the number of a certain type of local moves called direct self-tangency perestroika in a generic regular homotopy from a standard curve to a given one; the other basic local moves, namely inverse self- tangency perestroika and triple point crossing, do not change the value of J+. Thus, behavior of J+ under local moves is rather obvious. However, it is less understood how J+ behaves in the space of curves on a global scale. We study this problem using Legendrian knots, and give infinitely many regular homotopic curves with the same J+ that cannot be mutually related by inverse self-tangency perestroika and triple point crossing.

Original languageEnglish
Pages (from-to)1343-1357
Number of pages15
JournalIndiana University Mathematics Journal
Volume64
Issue number5
DOIs
Publication statusPublished - 2015
Externally publishedYes

Keywords

  • Legendrian knots
  • Plane curves
  • The Arnold invariants

ASJC Scopus subject areas

  • Mathematics(all)

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