### Abstract

In this note, we define a notion of finite-type for invariants of curves on surfaces as an analogue of the notion of finite-type for invariants of knots and 3-manifolds (Section 3). We also present a systematic construction for a large family of finite-type invariants SCI_{n} for curves on surfaces (Section 5). Arnold's invariants of plane isotopy classes of plane curves occur as invariants of order 1. Our theory of finite-type invariants of curves on surfaces is developed using the topological theory of words.

Original language | English |
---|---|

Pages (from-to) | 129-134 |

Number of pages | 6 |

Journal | Proceedings of the Japan Academy Series A: Mathematical Sciences |

Volume | 85 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2009 Nov |

### Keywords

- Arnold's invariants
- Finite-type invariants
- Immersed curves
- Topological theory of words

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Finite-type invariants for curves on surfaces'. Together they form a unique fingerprint.

## Cite this

Ito, N. (2009). Finite-type invariants for curves on surfaces.

*Proceedings of the Japan Academy Series A: Mathematical Sciences*,*85*(9), 129-134. https://doi.org/10.3792/pjaa.85.129