The geography problem for 4-manifolds with specified fundamental group

Details The geography problem for 4-manifolds with specified fundamental group The geography problem for 4-manifolds with specified fundamental group

2006-08-03

arxiv.org/abs/math/0608103v3

Trans. Amer. Math. Soc. 361 (2009), no. 8, 4091-4124

Mathematics

Geometric Topology

Minor expository changes. 33 pages, 6 figures

Scientific paper

For any given finitely presented group G there exists a closed oriented 4-manifold with fundamental group G. What pairs of integers can occur as the signature and Euler characteristic of such a 4-manifold? The first part of this paper develops general theory related to this question and applies this theory to resolve the question for a large collection of groups, including surface groups and 3-manifold groups. The second part of the paper offers an extended analysis in the case of free abelian groups, G = Z^n. The paper concludes with a list of open problems related to the general question.

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