doi:10.5427/jsing.2022.24eengArtal Bartolo, EnriqueWahl, JonathanFundamental Group of Rational Homology Disk Smoothings of Surface SingularitiesART-2022-130119It 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.2022http://zaguan.unizar.es/record/13140410.5427/jsing.2022.24ehttp://zaguan.unizar.es/record/131404oai:zaguan.unizar.es:131404info:eu-repo/grantAgreement/ES/DGA/E22-20Rinfo:eu-repo/grantAgreement/ES/MICINN/MTM2016-76868-C2-2-Pinfo:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033Journal of singularities 24 (2022), 126-144All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess