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.
|ジャーナル||Proceedings of the Japan Academy Series A: Mathematical Sciences|
|出版ステータス||Published - 2009 11|
ASJC Scopus subject areas
- 数学 (全般)