000131404 001__ 131404
000131404 005__ 20240209144726.0
000131404 0247_ $$2doi$$a10.5427/jsing.2022.24e
000131404 0248_ $$2sideral$$a130119
000131404 037__ $$aART-2022-130119
000131404 041__ $$aeng
000131404 100__ $$0(orcid)0000-0002-8276-5116$$aArtal Bartolo, Enrique$$uUniversidad de Zaragoza
000131404 245__ $$aFundamental Group of Rational Homology Disk Smoothings of Surface Singularities
000131404 260__ $$c2022
000131404 5060_ $$aAccess copy available to the general public$$fUnrestricted
000131404 5203_ $$aIt 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.
000131404 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2016-76868-C2-2-P$$9info:eu-repo/grantAgreement/ES/DGA/E22-20R
000131404 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000131404 592__ $$a0.339$$b2022
000131404 593__ $$aGeometry and Topology$$c2022$$dQ3
000131404 593__ $$aApplied Mathematics$$c2022$$dQ3
000131404 594__ $$a0.5$$b2022
000131404 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000131404 700__ $$aWahl, Jonathan
000131404 7102_ $$12006$$2440$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Geometría y Topología
000131404 773__ $$g24 (2022), 126-144$$tJournal of singularities$$x1949-2006
000131404 8564_ $$s435681$$uhttps://zaguan.unizar.es/record/131404/files/texto_completo.pdf$$yVersión publicada
000131404 8564_ $$s1928674$$uhttps://zaguan.unizar.es/record/131404/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000131404 909CO $$ooai:zaguan.unizar.es:131404$$particulos$$pdriver
000131404 951__ $$a2024-02-09-14:46:13
000131404 980__ $$aARTICLE