Regular embeddings of manifolds and topology of configuration spaces

Abstract

For a topological space $X$ we study continuous maps $f:X\to {\mathbb{R}}^m$ 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 ${\mathbb{R}}^n$ or $X$ is an $n$-dimensional manifold. In the latter case, some nonzero Stiefel--Whitney classes of $X$ help to improve the bound.

References in corpus (1)

• Multiplicity of continuous maps between manifolds