Volume 19, issue 5 (2015)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060

Nick Salter

Geometry & Topology 19 (2015) 2901–2923
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 3 we construct 4–manifolds E admitting at least n distinct fiberings pi: E Σgi 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
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
Authors
Nick Salter
Department of Mathematics
University of Chicago
5734 S University Avenue
Chicago, IL 60637
USA
http://math.uchicago.edu/~nks/