The geography problem for 4-manifolds with specified fundamental group

Kirk, Paul; Livingston, Charles

doi:10.1090/S0002-9947-09-04649-2

The geography problem for 4-manifolds with specified fundamental group
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by Paul Kirk and Charles Livingston PDF

Trans. Amer. Math. Soc. 361 (2009), 4091-4124 Request permission

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 $G$, the geography of $\mathcal {M}$ is the set of integer pairs $\{(\sigma (M), \chi (M)) | M \in \mathcal {M}\}$, 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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