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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Hausmann-Weinberger 4-manifold invariant of abelian groups


Authors: Paul Kirk and Charles Livingston
Journal: Proc. Amer. Math. Soc. 133 (2005), 1537-1546
MSC (2000): Primary 57M05, 57M07
Published electronically: October 18, 2004
MathSciNet review: 2111955
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Abstract: The Hausmann-Weinberger invariant of a group $G$ is the minimal Euler characteristic of a closed orientable 4-manifold $M$ with fundamental group $G$. We compute this invariant for finitely generated free abelian groups and estimate the invariant for all finitely generated abelian groups.


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Additional Information

Paul Kirk
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: pkirk@indiana.edu

Charles Livingston
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: livingst@indiana.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07652-X
PII: S 0002-9939(04)07652-X
Keywords: Hausmann-Weinberger invariant, fundamental group, four-manifold, minimal Euler characteristic
Received by editor(s): October 6, 2003
Received by editor(s) in revised form: December 31, 2003
Published electronically: October 18, 2004
Additional Notes: The first named author gratefully acknowledges the support of the National Science Foundation under grant no. DMS-0202148.
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.