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 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.
| 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)