#### Algebraic and Geometric Topology 2 (2002),
paper no. 20, pages 403-432.

## The fundamental group of a Galois cover of CP^1 X T

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

**Abstract**.
Let T be the complex projective torus, and X the surface CP^1 X 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(X_Gal) = Z^10.
**Keywords**.
Galois cover, fundamental group, generic projection, Moishezon-Teicher braid monodromy algorithm, Sieberg-Witten invariants

**AMS subject classification**.
Primary: 14Q10, 14J99.
Secondary: 14J80, 12F10.

**DOI:** 10.2140/agt.2002.2.403

**E-print:** `arXiv:math.AG/0205272`

Submitted: 15 March 2002.
(Revised: 9 May 2002.)
Accepted: 15 May 2002.
Published: 25 May 2002.

Notes on file formats
Meirav Amram and Mina Teicher:

Department of Mathematics,
Bar-Ilan University,
Ramat-Gan 52900, Israel

David Goldberg:

Department of Mathematics,
Colorado State University

Fort Collins, CO 80523-1874, USA

Uzi Vishne:

Einstein Institute of Mathematics,
Givat Ram Campus

The Hebrew University of Jerusalem,
Jerusalem 91904, Israel

Emails: amram@mi.uni-erlangen.de, meirav@macs.biu.ac.il, goldberg@math.colostate.edu, teicher@macs.biu.ac.il, vishne@math.huji.ac.il

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