Algebraic & Geometric Topology

On sections of hyperelliptic Lefschetz fibrations

Shunsuke Tanaka

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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.

Article information

Algebr. Geom. Topol., Volume 12, Number 4 (2012), 2259-2286.

Received: 6 March 2012
Revised: 10 August 2012
Accepted: 20 August 2012
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57N13: Topology of $E^4$ , $4$-manifolds [See also 14Jxx, 32Jxx]
Secondary: 20F34: Fundamental groups and their automorphisms [See also 57M05, 57Sxx]

4–manifold mapping class group Lefschetz fibration relation section Dehn twist monodromy hyperelliptic rational surface


Tanaka, Shunsuke. On sections of hyperelliptic Lefschetz fibrations. Algebr. Geom. Topol. 12 (2012), no. 4, 2259--2286. doi:10.2140/agt.2012.12.2259.

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