Virtual Betti numbers and the symplectic Kodaira dimension of fibered $4$-manifolds
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- by R. İnanç Baykur PDF
- Proc. Amer. Math. Soc. 142 (2014), 4377-4384 Request permission
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.References
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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
- MR Author ID: 794751
- Email: baykur@math.umass.edu
- 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
- © Copyright 2014 American Mathematical Society
- 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
- MathSciNet review: 3267005