# Regular embeddings of manifolds and topology of configuration spaces

@article{Karasev2010RegularEO, title={Regular embeddings of manifolds and topology of configuration spaces}, author={R. Karasev}, journal={arXiv: Algebraic Topology}, year={2010} }

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… CONTINUE READING

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