For a closed manifold , let be the number of ways that can be realized as a surface bundle, up to –fiberwise diffeomorphism. We consider the case when . We give the first computation of where but is not a product. In particular, we prove for the Atiyah–Kodaira manifold and any finite cover of a trivial surface bundle. We also give an example where .
"The number of fiberings of a surface bundle over a surface." Algebr. Geom. Topol. 18 (4) 2245 - 2263, 2018. https://doi.org/10.2140/agt.2018.18.2245