## 抄録

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.

本文言語 | English |
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ページ（範囲） | 1343-1357 |

ページ数 | 15 |

ジャーナル | Indiana University Mathematics Journal |

巻 | 64 |

号 | 5 |

DOI | |

出版ステータス | Published - 2015 |

外部発表 | はい |

## ASJC Scopus subject areas

- 数学 (全般)

## フィンガープリント

「A new aspect of the arnold invariant J^{+}from a global viewpoint」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。