Generators of the unoriented bordism ring which are fibered over products of projective spacesRP(2^r−1)

Abstract

For each positive integerk≦∞ we construct a family {M ⁿ_k } of generators of the unoriented bordims ring. The manifoldsM ⁿ_k are total spaces of fiber bundles whose base spaces are high-dimensional products of projective spaces$\mathbb{F}P\left( {2^{r_i } - 1} \right)$ wherer _i≦k. The fibers are themselves iterated projective bundles with maximal fiber dimension two. In the special casek=3 we obtain generatorsM ⁿ₃ which admit approximately 7/8·n pointwise linearly independent vector fields.