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# The Geography Problem for 4-Manifolds with Specified Fundamental Group

Paul Kirk and Charles Livingston
Transactions of the American Mathematical Society
Vol. 361, No. 8 (Aug., 2009), pp. 4091-4124
Stable URL: http://www.jstor.org/stable/40302690
Page Count: 34
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## Abstract

For any class M of 4-manifolds, for instance the class M(G) of closed oriented manifolds with $\pi _1 (M) \cong G$ for a fixed group G, the geography of M is the set of integer pairs {(σ(M), x(M)) | M ∈ M}, where σ and X denote the signature and Euler characteristic. This paper explores general properties of the geography of M(G) and undertakes an extended study of M(Zⁿ).

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