PreprintAn infrasolvmanifold which does not boundJ.A.HillmanAbstractOrientable 4dimensional infrasolvmanifolds bound orientably. We show that every nonorientable 4dimensional infrasolvmanifold \(M\) with \(\beta=\beta_1(M;\mathbb{Q})>0\) or with geometry \(\mathbb{N}il^3\) or \(\mathbb{S}ol^3\times\mathbb{E}^1\) bounds. However there are \(\mathbb{S}ol_1^4\)manifolds which are not boundaries. The question remains open for \(\mathbb{N}il^3\times\mathbb{E}^1\)manifolds. Any possible counterexamples have severely constrained fundamental groups. We also find simple cobounding 5manifolds for all but five of the 74 flat 4manifolds, and investigate which flat 4manifolds embed in \(\mathbb{R}^n\), for \(n=5,6\) or \(7\). Keywords: boundary, embedding, geometry, infrasolvmanifold, 4manifold.AMS Subject Classification: Primary 57R75.
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