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Recognizing products of surfaces and simply connected $ 4$-manifolds


Authors: Ian Hambleton and Matthias Kreck
Journal: Proc. Amer. Math. Soc. 143 (2015), 2253-2262
MSC (2010): Primary 57R55, 57R65
Published electronically: December 15, 2014
MathSciNet review: 3314132
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Abstract: We give necessary and sufficient conditions for a closed smooth $ 6$-manifold $ N$ to be diffeomorphic to a product of a surface $ F$ and a simply connected $ 4$-manifold $ M$ in terms of basic invariants like the fundamental group and cohomological data. Any isometry of the intersection form of $ M$ is realized by a self-diffeomorphism of $ M \times F$.


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Additional Information

Ian Hambleton
Affiliation: Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1, Canada
Email: hambleton@mcmaster.ca

Matthias Kreck
Affiliation: Mathematisches Institut, Universität Bonn, D-53115 Bonn, Germany
Email: kreck@math.uni-bonn.de

DOI: https://doi.org/10.1090/S0002-9939-2014-12425-7
Received by editor(s): March 17, 2013
Received by editor(s) in revised form: October 4, 2013, and November 7, 2013
Published electronically: December 15, 2014
Additional Notes: This research was partially supported by NSERC Discovery Grant A4000. The authors wish to thank the Max Planck Institut für Mathematik in Bonn for its hospitality and support
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2014 American Mathematical Society