抄録
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 SCIn 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.
| 本文言語 | English |
|---|---|
| ページ（範囲） | 129-134 |
| ページ数 | 6 |
| ジャーナル | Proceedings of the Japan Academy Series A: Mathematical Sciences |
| 巻 | 85 |
| 号 | 9 |
| DOI | |
| 出版ステータス | Published - 2009 11月 |
ASJC Scopus subject areas
- 数学 (全般)