The geography problem for 4-manifolds with specified fundamental group

Paul Kirk; Charles Livingston

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The geography problem for 4-manifolds with specified fundamental group

Paul Kirk·Charles Livingston

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Abstract

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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BibTeX RIS

Paul Kirk, Charles Livingston. 2006-10-10. The geography problem for 4-manifolds with specified fundamental group. https://arxiv.org/abs/math/0608103

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