On sections of hyperelliptic Lefschetz fibrations

Tanaka, Shunsuke

doi:10.2140/agt.2012.12.2259

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On sections of hyperelliptic Lefschetz fibrations

Shunsuke Tanaka

Algebraic & Geometric Topology 12 (2012) 2259–2286

DOI: 10.2140/agt.2012.12.2259

Abstract

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

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

Volume 12, issue 4 (2012)