The number of fiberings of a surface bundle over a surface

Abstract

For a closed manifold $M$, let Fib$(M)$ be the number of distinct fiberings of $M$ as a fiber bundle with fiber a closed surface. In this paper we give the first computation of Fib$(M)$ where $1<\text{Fib}(M)<\infty$ but $M$ is not a product. In particular, we prove Fib$(M)=2$ for the Atiyah-Kodaira manifold and any finite cover of a trivial surface bundle. We also give an example where Fib$(M)=4$.

16 pages, 4 figures

References in corpus (2)

• Cup products, the Johnson homomorphism, and surface bundles over surfaces with multiple fiberings
• The universal $n$-pointed surface bundle only has $n$ sections

Cited by in corpus (3)

• Mapping class groups, multiple Kodaira fibrations, and CAT(0) spaces
• Reduced resonance schemes and Chen ranks
• Arithmeticity of the monodromy of some Kodaira fibrations