The Coxeter quotient of the fundamental group of a Galois cover of T \times T

Amram Meirav; Mina Teicher; Uzi Vishne

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The Coxeter quotient of the fundamental group of a Galois cover of T \times T

Amram Meirav·Mina Teicher·Uzi Vishne

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Abstract

Let $X$ be the surface $\T\times\T$ 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.

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BibTeX RIS

Amram Meirav, Mina Teicher, Uzi Vishne. 2009-03-23. The Coxeter quotient of the fundamental group of a Galois cover of T \times T. https://arxiv.org/abs/math/0404459

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