The Coxeter quotient of the fundamental group of a Galois cover of T × T

2004/04/26 by Meirav, Amram, Teicher, Mina, Vishne, Uzi
#14J29 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.math/0404459

Abstract

Let X be the surface \T×\T where \T is the complex torus. This paper is the third in a series, studying the fundamental group of the Galois cover of X \wrt a generic projection onto \C¶². Van Kampen Theorem gives a presentation of the fundamental group of the complement of the branch curve, with 54 generators and more than 2000 relations. Here we introduce a certain natural quotient (obtained by identifying pairs of generators), prove it is a quotient of a Coxeter group related to the degeneration of X, and show that this quotient is virtually nilpotent.

Related

• The fundamental group of Galois cover of the surface \mathbb T × \mathbb T
• The fundamental group of the complement of the branch curve of T times T in C²
• Classification of Fundamental Groups of Galois Covers of Surfaces of Small Degree Degenerating to Nice Plane Arrangements
• Fundamental group of Galois covers of degree 5 surfaces
• The fundamental group of compact Riemann surface