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2018 The number of fiberings of a surface bundle over a surface
Lei Chen
Algebr. Geom. Topol. 18(4): 2245-2263 (2018). DOI: 10.2140/agt.2018.18.2245

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 π 1 –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 .

Citation

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Lei Chen. "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

Information

Received: 31 March 2017; Revised: 21 December 2017; Accepted: 18 January 2018; Published: 2018
First available in Project Euclid: 3 May 2018

zbMATH: 06867657
MathSciNet: MR3797066
Digital Object Identifier: 10.2140/agt.2018.18.2245

Subjects:
Primary: 57M50, 57R22
Secondary: 55N25, 57M10

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 4 • 2018
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