Geometric monodromy and the hyperbolic disc

Details Geometric monodromy and the hyperbolic disc Geometric monodromy and the hyperbolic disc

2000-11-27

arxiv.org/abs/math/0011223v1

Mathematics

Symplectic Geometry

13 pages. [To appear in Quarterly J. Math. (Oxford)]

Scientific paper

Symplectic four-manifolds give rise to Lefschetz fibrations, which are determined by monodromy representations of free groups in mapping class groups. We study the topology of Lefschetz fibrations by analysing the action of the monodromy on the universal cover of a smooth fibre. We give new and simple proofs that Lefschetz fibrations arising from pencils (i.e. with exceptional sections) never split as non-trivial fibre sums, and that no simple closed curve can be invariant to isotopy under the monodromy representation.

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