Fundamental Group of Rational Homology Disk Smoothings of Surface Singularities

Artal Bartolo, Enrique (Universidad de Zaragoza) ; Wahl, Jonathan

Resumen: It is known that there are exactly three triply-infinite and seven singly-infinite families of weighted homogeneous normal surface singularities admitting a rational homology disk smoothing, i.e., having a Milnor fibre with Milnor number zero. Some examples are found by an explicit “quotient construction”, while others require the “Pinkham method”. The fundamental group of the Milnor fibre has been known for all except three exceptional families. In this paper, we settle these cases. We present a new explicit construction for one of the exceptional families, showing the fundamental group is non-abelian (as occurred previously only for three families). We show that the fundamental groups for the remaining two exceptional families are abelian, hence easily computed; using the Pinkham method here requires precise calculations for the fundamental group of the complement of a plane curve.

Idioma: Inglés

DOI: 10.5427/jsing.2022.24e

Año: 2022

Publicado en: Journal of singularities 24 (2022), 126-144
ISSN: 1949-2006

Factor impacto CITESCORE: 0.5 - Mathematics (Q4)

Factor impacto SCIMAGO: 0.339 - Geometry and Topology (Q3) - Applied Mathematics (Q3)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E22-20R
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2016-76868-C2-2-P
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)