Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 50, No. 2, pp. 469482 (2009) 

The fundamental group for the complement of Cayley's singularitiesMeirav Amram, Michael Dettweiler, Michael Friedman and Mina TeicherEinstein Mathematics Institute, Hebrew University, Jerusalem, Israel and Mathematics Department, BarIlan University, Israel, email: ameirav@math.huji.ac.il, meirav@macs.biu.ac.il; IWR, Heidelberg University, Germany, email: michael.dettweiler@iwr.uniheidelberg.de; Mathematics Department, BarIlan Un iversity, Israel, email: fridmam@macs.biu.ac.il email: teicher@macs.biu.ac.ilAbstract: Given a singular surface $X$, one can extract information on it by investigating the fundamental group $\pi_1(X  Sing_X)$. However, calculation of this group is nontrivial, but it can be simplified if a certain invariant of the branch curve of $X$  called the braid monodromy factorization  is known. This paper shows, taking the Cayley cubic as an example, how this fundamental group can be computed by using braid monodromy techniques ([M]) and their liftings. This is one of the first examples that uses these techniques to calculate this sort of fundamental group. [M] Moishezon, B.; Teicher, M.: {\em Braid group technique in complex geometry I. Line arrangements in $\C\P^2$}. Contemp. Math. {\bf 78} (1988), 425555. Keywords: singularities, coverings, fundamental groups, surfaces, mapping class group Classification (MSC2000): 14B05, 14E20, 14H30, 14Q10 Full text of the article:
Electronic version published on: 28 Aug 2009. This page was last modified: 28 Jan 2013.
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