Abstract
In the light of recent results it turns out that both closed symplectic 4-manifolds and Stein surfaces admit a purely topological description in terms of Lefschetz fibrations and Lefschetz pencils. In this chapter we give the necessary definitions and sketch this topological descriptions of symplectic and Stein manifolds. In the discussion we include achiral Lefschetz fibrations as well; these more general objects are useful in viewing open book decompositions as boundaries of certain achiral Lefschetz fibrations. The chapter concludes with some applications of Lefschetz fibrations in various low dimensional problems.
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© 2004 Springer-Verlag Berlin Heidelberg
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Ozbagci, B., Stipsicz, A.I. (2004). Lefschetz Fibrations on 4-Manifolds. In: Surgery on Contact 3-Manifolds and Stein Surfaces. Bolyai Society Mathematical Studies, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10167-4_10
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DOI: https://doi.org/10.1007/978-3-662-10167-4_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-06184-4
Online ISBN: 978-3-662-10167-4
eBook Packages: Springer Book Archive