Transactions of the American Mathematical Society

Author(s): Paul Kirk; Charles Livingston
Journal: Trans. Amer. Math. Soc. 361 (2009), 4091-4124.
MSC (2000): Primary 57M05, 57N13, 57R19
Posted: March 16, 2009
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Abstract: For any class $\mathcal{M}$ of 4-manifolds, for instance the class $\mathcal{M}(G)$ of closed oriented manifolds with $\pi_1(M) \cong G$ for a fixed group

, the geography of $\mathcal{M}$ is the set of integer pairs $\{(\sigma(M), \chi(M)) \vert M \in \mathcal{M}\}$ , where $\sigma$ and $\chi$ denote the signature and Euler characteristic. This paper explores general properties of the geography of $\mathcal{M}(G)$ and undertakes an extended study of $\mathcal{M}(\mathbf{Z}^n)$ .

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 57M05, 57N13, 57R19

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/S0002-9947-09-04649-2
PII: S 0002-9947(09)04649-2
Keywords: Hausmann-Weinberger invariant, fundamental group, four-manifold, minimal Euler characteristic, geography
Received by editor(s): May 25, 2007
Posted: March 16, 2009
Additional Notes: This work was supported by grants from the NSF
Copyright of article: Copyright 2009, American Mathematical Society

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