The geography problem for 4-manifolds with specified fundamental group. (English) Zbl 1177.57020
Authors’ summary: 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 \( \mathcal{M}(\mathbb Z^n)\).
Reviewer: Alberto Cavicchioli (Modena)
MSC:
| 57N13 | Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010) |
| 57M05 | Fundamental group, presentations, free differential calculus |
| 57R19 | Algebraic topology on manifolds and differential topology |
Keywords:
Hausmann-Weinberger invariant; fundamental group; four-manifold; minimal Euler characteristic; geographyReferences:
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