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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 1 × T. Let XGal be its Galois cover with respect to a generic projection to 2. In this paper we compute the fundamental group of XGal, using the degeneration and regeneration techniques, the Moishezon-Teicher braid monodromy algorithm and group calculations. We show that π1(XGal) = 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
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Publication
Received: 15 March 2002
Revised: 9 May 2002
Accepted: 15 May 2002
Published: 25 May 2002
Authors
Meirav Amram
Department of Mathematics, Bar-Ilan University Ramat-Gan 52900
Israel
David Goldberg
Department of Mathematics
Bar-Ilan University
Ramat-Gan 52900
Israel
Mina Teicher
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