Do almost flat manifolds bound?
The long standing conjecture that flat manifolds bound was proved by \textit{G. C. Hamrick} and \textit{D. C. Royster} [Invent. Math. 66, 405-413 (1982; Zbl 0476.57018]. The present authors take up the interesting problem whether the same thing holds for almost flat manifolds in the sense of \textit{M. Gromov} [J. Differ. Geom. 13, 231-241 (1978; Zbl 0432.53020)]. Their main result is that this is indeed the case if the fundamental group \(\pi_ 1(M)\) of the almost flat manifold M contains a nilpotent subgroup of index either m or 2m, where m is an odd integer.
scientific article; zbMATH DE number 3864034