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The Hausmann-Weinberger 4-manifold invariant of abelian groups

Author(s): Paul Kirk; Charles Livingston
Journal: Proc. Amer. Math. Soc. 133 (2005), 1537-1546.
MSC (2000): Primary 57M05, 57M07
Posted: October 18, 2004
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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: 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
Posted: 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
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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