Regular embeddings of manifolds and topology of configuration spaces

الأصل · EN

For a topological space X we study continuous maps f: X→ Rᵐ such that images of every pairwise distinct k points are affinely (linearly) independent. Such maps are called affinely (linearly) k-regular embeddings. We investigate the cohomology obstructions to existence of regular embeddings and give some new lower bounds on the dimension m as function of X and k, for the cases X is Rⁿ or X is an n-dimensional manifold. In the latter case, some nonzero Stiefel--Whitney classes of X help to improve the bound.