Finite-type invariants for curves on surfaces

Noboru Ito

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 languageEnglish
Pages (from-to)129-134
Number of pages6
JournalProceedings of the Japan Academy Series A: Mathematical Sciences
Volume85
Issue number9
DOIs
Publication statusPublished - 2009 Nov

Fingerprint

Finite Type Invariants
Curve
Invariant
Finite Type
Isotopy
Plane Curve
Knot
Analogue

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Finite-type invariants for curves on surfaces. / Ito, Noboru.

In: Proceedings of the Japan Academy Series A: Mathematical Sciences, Vol. 85, No. 9, 11.2009, p. 129-134.

Research output: Contribution to journalArticle

@article{6c2f73ed973543efb22eb312352ca47b,
title = "Finite-type invariants for curves on surfaces",
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.",
keywords = "Arnold's invariants, Finite-type invariants, Immersed curves, Topological theory of words",
author = "Noboru Ito",
year = "2009",
month = "11",
doi = "10.3792/pjaa.85.129",
language = "English",
volume = "85",
pages = "129--134",
journal = "Proceedings of the Japan Academy Series A: Mathematical Sciences",
issn = "0386-2194",
publisher = "Japan Academy",
number = "9",

}

TY - JOUR

T1 - Finite-type invariants for curves on surfaces

AU - Ito, Noboru

PY - 2009/11

Y1 - 2009/11

N2 - 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.

AB - 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.

KW - Arnold's invariants

KW - Finite-type invariants

KW - Immersed curves

KW - Topological theory of words

UR - http://www.scopus.com/inward/record.url?scp=77949338454&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949338454&partnerID=8YFLogxK

U2 - 10.3792/pjaa.85.129

DO - 10.3792/pjaa.85.129

M3 - Article

VL - 85

SP - 129

EP - 134

JO - Proceedings of the Japan Academy Series A: Mathematical Sciences

JF - Proceedings of the Japan Academy Series A: Mathematical Sciences

SN - 0386-2194

IS - 9

ER -