#### Volume 2, issue 1 (2002)

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The fundamental group of a Galois cover of $\mathbb{CP}^1 \times T$

### Meirav Amram, David Goldberg, Mina Teicher and Uzi Vishne

Algebraic & Geometric Topology 2 (2002) 403–432
 arXiv: math.AG/0205272
##### Abstract

Let $T$ be the complex projective torus, and $X$ the surface ${ℂℙ}^{1}×T$. Let ${X}_{Gal}$ be its Galois cover with respect to a generic projection to ${ℂℙ}^{2}$. In this paper we compute the fundamental group of ${X}_{Gal}$, using the degeneration and regeneration techniques, the Moishezon-Teicher braid monodromy algorithm and group calculations. We show that ${\pi }_{1}\left({X}_{Gal}\right)={ℤ}^{10}$.

##### Keywords
Galois cover, fundamental group, generic projection, Moishezon–Teicher braid monodromy algorithm, Sieberg-Witten invariants
##### Mathematical Subject Classification 2000
Primary: 14Q10, 14J99
Secondary: 14J80, 32Q55