Volume 18, issue 4 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 19
Issue 6, 2677–3215
Issue 5, 2151–2676
Issue 4, 1619–2150
Issue 3, 1079–1618
Issue 2, 533–1078
Issue 1, 1–532

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

Author Index
The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
To Appear
 
Other MSP Journals
The number of fiberings of a surface bundle over a surface

Lei Chen

Algebraic & Geometric Topology 18 (2018) 2245–2263
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 π1 –fiberwise diffeomorphism. We consider the case when dim(M) = 4. We give the first computation of SFib(M) where 1 < SFib(M) < 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