Finite-type invariants for curves on surfaces

Noboru Ito*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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 languageEnglish
Pages (from-to)129-134
Number of pages6
JournalProceedings of the Japan Academy Series A: Mathematical Sciences
Issue number9
Publication statusPublished - 2009 Nov


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

ASJC Scopus subject areas

  • General Mathematics


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