Finite-type invariants for curves on surfaces

Finite-type invariants for curves on surfaces

Noboru Ito

Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 85, Number 9 (2009), 129-134.

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.

Primary Subjects: 57M99

Keywords: Finite-type invariants; immersed curves; topological theory of words; Arnold's invariants

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pja/1257430680
Digital Object Identifier: doi:10.3792/pjaa.85.129

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