Surface bundles over surfaces with arbitrarily many fiberings

Salter, Nick

doi:10.2140/gt.2015.19.2901

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Surface bundles over surfaces with arbitrarily many fiberings

Nick Salter

Geometry & Topology 19 (2015) 2901–2923

DOI: 10.2140/gt.2015.19.2901

Correction: 10.2140/gt.2021.25.2707

Abstract

In this paper we give the first example of a surface bundle over a surface with at least three fiberings. In fact, for each $n \geq 3$ we construct $4$ –manifolds $E$ admitting at least $n$ distinct fiberings $p_{i} : E \to Σ_{g_{i}}$ as a surface bundle over a surface with base and fiber both closed surfaces of negative Euler characteristic. We give examples of surface bundles admitting multiple fiberings for which the monodromy representation has image in the Torelli group, showing the necessity of all of the assumptions made in the main theorem of a recent paper of ours. Our examples show that the number of surface bundle structures that can be realized on a $4$ –manifold $E$ with Euler characteristic $d$ grows exponentially with $d$ .

Keywords

surface bundles

Mathematical Subject Classification 2010

Primary: 57R22

References

Publication

Received: 4 August 2014

Revised: 25 January 2015

Accepted: 2 March 2015

Published: 20 October 2015

Proposed: Shigeyuki Morita

Seconded: Walter Neumann, Ronald Stern

Correction: 3 September 2021

Authors

Nick Salter
Department of Mathematics University of Chicago 5734 S University Avenue Chicago, IL 60637 USA
http://math.uchicago.edu/~nks/

Volume 19, issue 5 (2015)