All flat three-manifolds appear as cusps of hyperbolic four-manifolds (Q1295192)

It was conjectured [see \textit{F. T. Farrell} and \textit{S. Zdravkovska}, Mich. Math. J. 30 199-208 (1983; Zbl 0543.53037)] that every diffeomorphism class of compact flat manifolds occurs as the boundary of a manifold whose interior admits a complete hyperbolic structure of finite volume. This conjecture was motivated by earlier work of \textit{M. L. Gromov} [J. Differ. Geom. 13, 223-230 (1978; Zbl 0433.53028)], 231-241 (1978; Zbl 0432.53020)]. The author provides evidence in support of this conjecture. In particular, she proves that each diffeomorphism class of compact flat 3-manifolds appears as one of the cusps of a complete finite-volume hyperbolic 4-manifold. Then some applications are obtained about the geometric structures which can be induced on cusps of complete finite-volume hyperbolic 4-manifolds.