Vanishing of higher order Alexander-type invariants of plane curves

Cogolludo Agustín, José Ignacio (Universidad de Zaragoza) ; Elduque, Eva

Resumen: The higher order degrees are Alexander-type invariants of complements to an affine plane curve. In this paper, we characterize the vanishing of such invariants for a curve given as a transversal union of plane curves ′ and ′′ in terms of the finiteness and the vanishing properties of the invariants of ′ and ′′, and whether or not they are irreducible. As a consequence, we prove that the multivariable Alexander polynomial Δmulti is a power of ( − 1), and we characterize when Δmulti = 1 in terms of the defining equations of ′ and ′′. Our results impose obstructions on the class of groups that can be realized as fundamental groups of complements of a transversal union of curves.

Idioma: Inglés

DOI: 10.1002/mana.202100610

Año: 2023

Publicado en: Mathematische Nachrichten 296, 3 (2023), 1026-1040
ISSN: 0025-584X

Factor impacto JCR: 0.8 (2023)

Categ. JCR: MATHEMATICS rank: 179 / 490 = 0.365 (2023) - Q2 - T2

Factor impacto CITESCORE: 1.5 - Mathematics (all) (Q2)

Factor impacto SCIMAGO: 0.625 - Mathematics (miscellaneous) (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E22-20R
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033

Tipo y forma: Article (Published version)

Área (Departamento): Área Geometría y Topología (Dpto. Matemáticas)