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Virtual Betti numbers and the symplectic Kodaira dimension of fibered $ 4$-manifolds


Author: R. İnanç Baykur
Journal: Proc. Amer. Math. Soc. 142 (2014), 4377-4384
MSC (2010): Primary 57M05, 57R17
DOI: https://doi.org/10.1090/S0002-9939-2014-12151-4
Published electronically: August 14, 2014
MathSciNet review: 3267005
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that if a closed oriented $ 4$-manifold $ X$ fibers over a $ 2$- or $ 3$-dimensional manifold, in most cases all of its virtual Betti numbers are infinite. In turn, we show that a closed oriented $ 4$-manifold $ X$ which is not a tower of torus bundles and fibering over a $ 2$- or $ 3$-dimensional manifold does not admit a torsion symplectic canonical class, nor is it of Kodaira dimension zero.


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Additional Information

R. İnanç Baykur
Affiliation: Max Planck Institute for Mathematics, Bonn, Germany – and – Department of Mathematics, Brandeis University, Waltham, Massachusetts 02453
Address at time of publication: Department of Mathematics & Statistics, University of Massachusetts Amherst, Amherst, Massachusetts 01003
Email: baykur@math.umass.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12151-4
Received by editor(s): October 24, 2012
Received by editor(s) in revised form: January 26, 2013
Published electronically: August 14, 2014
Additional Notes: The author was partially supported by the NSF grant DMS-0906912.
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2014 American Mathematical Society

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