131404 20240209144726.0 doi 10.5427/jsing.2022.24e sideral 130119 ART-2022-130119 eng Artal Bartolo, Enrique Universidad de Zaragoza (orcid)0000-0002-8276-5116 Fundamental Group of Rational Homology Disk Smoothings of Surface Singularities 2022 Access copy available to the general public Unrestricted 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. info:eu-repo/grantAgreement/ES/DGA/E22-20R info:eu-repo/grantAgreement/ES/MICINN/MTM2016-76868-C2-2-P info:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033 info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 0.339 2022 Geometry and Topology 2022 Q3 Applied Mathematics 2022 Q3 0.5 2022 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Wahl, Jonathan 2006 440 Universidad de Zaragoza Dpto. Matemáticas Área Geometría y Topología 24 (2022), 126-144 Journal of singularities 1949-2006 435681 http://zaguan.unizar.es/record/131404/files/texto_completo.pdf Versión publicada 1928674 http://zaguan.unizar.es/record/131404/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:131404 articulos driver 2024-02-09-14:46:13 ARTICLE