2014/02/23 by Gleb Nenashev, Nenashev, Gleb
Computer Science · Mathematics · #05C10 #52C30 #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.CO #math.DG #msc:05C10 #msc:52C30
paper · pdf · doi:10.48550/arxiv.1402.5659
8 pages
arxiv created 2014/02/23 · openalex publication_date 2014/02/23 · arxiv updated 2014/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a plane curve γ: S1→ \mathbb R2, we consider the problem of determining the minimal number I(γ) of inflections which curves diff(γ) may have, where diff runs over the group of diffeomorphisms of \mathbb R2. We show that if γ is an immersed curve with D(γ) double points and no other singularities, then I(γ)≤ 2D(γ). In fact, we prove the latter result for the so-called plane doodles which are finite collections of closed immersed plane curves whose only singularities are double points.