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

Autor:	Gergő Pintér, András Sándor
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	Mathematics - Algebraic Geometry Mathematics - Complex Variables General Mathematics FOS: Mathematics Algebraic Topology (math.AT) 32Sxx 57Rxx (Primary) 57Nxx 57Nxx (Secondary) Mathematics - Algebraic Topology Complex Variables (math.CV) Algebraic Geometry (math.AG)
Popis:	It was recently proved that for finitely determined germs $ \Phi: ( \mathbb{C}^2, 0) \to ( \mathbb{C}^3, 0) $ the number $C(\Phi)$ of Whitney umbrella points and the number $T(\Phi)$ of triple values of a stable deformation are topological invariants. The proof uses the fact that the combination $C(\Phi)-3T(\Phi)$ is topological since it equals the linking invariant of the associated immersion $S^3 \looparrowright S^5$ introduced by Ekholm and Sz\H{u}cs. We provide a new, direct proof for this equality. We also clarify the relation between various definitions of the latter invariant. Comment: 13 page, 2 figures
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::befcba75e44a389111c729c36507e8e6 http://arxiv.org/abs/2202.05828 Zobrazit plný text záznamu