Fundamental group of rational homology disk smoothings of surface singularities
Journal of Singularities, Tome 24 (2022), pp. 126-144
Voir la notice de l'article provenant de la source Journal of Singularities website
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.
@article{10_5427_jsing_2022_24e,
author = {Enrique Artal Bartolo and Jonathan Wahl},
title = {Fundamental group of rational homology disk smoothings of surface singularities},
journal = {Journal of Singularities},
pages = {126--144},
publisher = {mathdoc},
volume = {24},
year = {2022},
doi = {10.5427/jsing.2022.24e},
url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2022.24e/}
}
TY - JOUR AU - Enrique Artal Bartolo AU - Jonathan Wahl TI - Fundamental group of rational homology disk smoothings of surface singularities JO - Journal of Singularities PY - 2022 SP - 126 EP - 144 VL - 24 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.5427/jsing.2022.24e/ DO - 10.5427/jsing.2022.24e ID - 10_5427_jsing_2022_24e ER -
%0 Journal Article %A Enrique Artal Bartolo %A Jonathan Wahl %T Fundamental group of rational homology disk smoothings of surface singularities %J Journal of Singularities %D 2022 %P 126-144 %V 24 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.5427/jsing.2022.24e/ %R 10.5427/jsing.2022.24e %F 10_5427_jsing_2022_24e
Enrique Artal Bartolo; Jonathan Wahl. Fundamental group of rational homology disk smoothings of surface singularities. Journal of Singularities, Tome 24 (2022), pp. 126-144. doi: 10.5427/jsing.2022.24e
Cité par Sources :