Aspherical manifolds with boundary

James F. Davis; J. A. Hillman

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arXiv · 2501.12509

Aspherical manifolds with boundary

James F. Davis·J. A. Hillman

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Abstract

We undertake a systematic investigation of compact aspherical manifolds with boundary; motivated by the plethora of examples in the bounded case and by the beauty of the theory in the closed case. Our main theorems give a homological criterion for when a closed manifold, together with maps from the fundamental groups of its components to a fixed group, can be realized as the boundary of a compact aspherical manifold. This is done in two steps: we first produce a Poincar\'e pair and then apply surgery theory to obtain a manifold. We illustrate this in the case of abelian fundamental group. The results of this paper will be applied in a sequel where we classify compact aspherical 4-manifolds with elementary amenable fundamental group.

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BibTeX RIS

James F. Davis, J. A. Hillman. 2025-01-21. Aspherical manifolds with boundary. https://arxiv.org/abs/2501.12509

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