The number of fiberings of a surface bundle over a surface

Chen, Lei

doi:10.2140/agt.2018.18.2245

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The number of fiberings of a surface bundle over a surface

Lei Chen

Algebraic & Geometric Topology 18 (2018) 2245–2263

DOI: 10.2140/agt.2018.18.2245

Abstract

For a closed manifold $M$ , let $SFib (M)$ be the number of ways that $M$ can be realized as a surface bundle, up to $π_{1}$ –fiberwise diffeomorphism. We consider the case when $dim (M) = 4$ . We give the first computation of $SFib (M)$ where $1 < SFib (M) < \infty$ 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 $SFib (M) = 4$ .

Keywords

surface bundle, branched cover

Mathematical Subject Classification 2010

Primary: 57R22, 57M50

Secondary: 57M10, 55N25

References

Publication

Received: 31 March 2017

Revised: 21 December 2017

Accepted: 18 January 2018

Published: 26 April 2018

Authors

Lei Chen
Department of Mathematics University of Chicago Chicago, IL United States
http://math.uchicago.edu/~chenlei

Volume 18, issue 4 (2018)