Volume 12, issue 4 (2012)

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On sections of hyperelliptic Lefschetz fibrations

Shunsuke Tanaka

Algebraic & Geometric Topology 12 (2012) 2259–2286
Abstract

We construct a relation among right-handed Dehn twists in the mapping class group of a compact oriented surface of genus $g$ with $4g+4$ boundary components. This relation gives an explicit topological description of $4g+4$ disjoint $\left(-1\right)$–sections of a hyperelliptic Lefschetz fibration of genus $g$ on the manifold ${ℂℙ}^{2}#\left(4g+5\right){\overline{ℂℙ}}^{2}$.

Keywords
4–manifold, mapping class group, Lefschetz fibration, relation, section, Dehn twist, monodromy, hyperelliptic, rational surface
Primary: 57N13
Secondary: 20F34
Publication
Revised: 10 August 2012
Accepted: 20 August 2012
Published: 5 January 2013
Authors
 Shunsuke Tanaka Department of Mathematics Graduate School of Science Osaka University Osaka 560-0043 Japan