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Summary: math.GT/9810042
v2
25
Nov
1998
Symplectic Lefschetz fibrations with arbitrary fundamental groups
J. Amor'os \Lambda , F. Bogomolov y , L. Katzarkov z , T. Pantev x
(with an appendix by Ivan Smith)
Abstract
In this paper we give an explicit construction of a symplectic Lefschetz fibration whose total
space is a smooth compact four dimensional manifold with a prescribed fundamental group. We
also study the numerical properties of the sections in symplectic Lefschetz fibrations and their
relation to the structure of the monodromy group.
Contents
1 Introduction 2
Notation and terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Symplectic Lefschetz fibrations 5
3 The main construction 9
3.1 Positive relations among right Dehn twists . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 Geometric presentations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
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