The bounding problem for infra-solvmanifolds

The conjecture that every n  -dimensional almost flat manifold (equivalently, infra-nilmanifold) is the boundary of an (n+1)(n+1)-dimensional manifold has been long open. We propose the more general conjecture that every n-dimensional infra-solvmanifold bounds, which is true in dimensions less than 5. Davis and Fang show that every infra-nilmanifold with cyclic or generalized quaternionic holonomy bound. We extend these results to certain infra-nilmanifolds with holonomy a dihedral group or direct product of two cyclic groups, and generalize them to the setting of infra-solvmanifolds modeled on solvable Lie groups with non-trivial center.