2000/11/27 by Ivan Smith, Smith, Ivan
Mathematics · #53C15 #FOS: Mathematics #Symplectic Geometry (math.SG) #math.SG #msc:53C15
paper · pdf · doi:10.48550/arxiv.math/0011223
13 pages. [To appear in Quarterly J. Math. (Oxford)]
arxiv created 2000/11/27 · arxiv updated 2009/11/30
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.