Volume 18, issue 4 (2018)

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The number of fiberings of a surface bundle over a surface

Lei Chen

Algebraic & Geometric Topology 18 (2018) 2245–2263

For a closed manifold M, let SFib(M) be the number of ways that M can be realized as a surface bundle, up to π1 –fiberwise diffeomorphism. We consider the case when dim(M) = 4. We give the first computation of SFib(M) where 1 < SFib(M) < but M is not a product. In particular, we prove SFib(M) = 2 for the Atiyah–Kodaira manifold and any finite cover of a trivial surface bundle. We also give an example where SFib(M) = 4.

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surface bundle, branched cover
Mathematical Subject Classification 2010
Primary: 57R22, 57M50
Secondary: 57M10, 55N25
Received: 31 March 2017
Revised: 21 December 2017
Accepted: 18 January 2018
Published: 26 April 2018
Lei Chen
Department of Mathematics
University of Chicago
Chicago, IL
United States