English

Introduction to Arnold's $J^+$-Invariant

Differential Geometry 2022-10-04 v1 Symplectic Geometry

Abstract

We explore Arnold's J+J^+-invariant of immersions -- planar smooth closed curves with non-vanishing derivative, at most double points and only transverse intersections -- and computation methods like Viro's sum, among others. Only basic undergraduate mathematics is needed to understand the contents of this introductory paper and everything we need that is above that is recalled or introduced. Examples, exercises and solutions are included for practice.

Keywords

Cite

@article{arxiv.2210.00871,
  title  = {Introduction to Arnold's $J^+$-Invariant},
  author = {Alexander Mai},
  journal= {arXiv preprint arXiv:2210.00871},
  year   = {2022}
}

Comments

38 pages, 52 figures, for figure files see https://gitlab.com/CptMaister/paper-intro-to-j-plus

R2 v1 2026-06-28T02:36:00.220Z