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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 (1)–sections of a hyperelliptic Lefschetz fibration of genus g on the manifold 2 # (4g + 5)¯2.

Keywords
4–manifold, mapping class group, Lefschetz fibration, relation, section, Dehn twist, monodromy, hyperelliptic, rational surface
Mathematical Subject Classification 2010
Primary: 57N13
Secondary: 20F34
References
Publication
Received: 6 March 2012
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