Immersions and embeddings of quasitoric manifolds over the cube (Q2815244)

The author considers quasitoric manifolds over the cube \(I^n\). The characteristic matrices are conveniently chosen, in order to achieve that the corresponding quasitoric manifolds have nonzero dual Stiefel-Whitney classes in pretty high dimensions. These nontrivial classes provide lower bounds for the minimal dimension of Euclidean space in which the given manifold can be embedded, immersed or totally skew embedded. Moreover, when \(n\) is a power of two, the obtained lower bounds for embeddings and immersions are shown to be the best possible.