Cross-caps, triple points and a linking invariant for finitely determined germs

2022/02/11 by Gergő Pintér, Pintér, Gergő, András Sándor +1
Mathematics · #32Sxx #57Nxx (Secondary) #57Rxx (Primary) 57Nxx #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Complex Variables (math.CV) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2202.05828

openalex publication_date 2022/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It was recently proved that for finitely determined germs Φ: ( ℂ², 0) → ( ℂ³, 0) the number C(Φ) of Whitney umbrella points and the number T(Φ) of triple values of a stable deformation are topological invariants. The proof uses the fact that the combination C(Φ)-3T(Φ) is topological since it equals the linking invariant of the associated immersion S³ \looparrowright S⁵ introduced by Ekholm and Szűcs. We provide a new, direct proof for this equality. We also clarify the relation between various definitions of the latter invariant.

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