On $r$-neighborly submanifolds in $R^N$

Victor A. Vassiliev

On $r$-neighborly submanifolds in $R^N$

Geometric Topology 2014-07-29 v1 Algebraic Topology Combinatorics

Authors: Victor A. Vassiliev

Abstract

A submanifold $M \subset R^N$ is $r$ -neighborly if for any $r$ points in $M$ there is a hyperplane, supporting $M$ and touching it at exactly these $r$ points. We prove that the minimal dimension $\Delta(k,r)$ of the Euclidean space, containing a stably $r$ -neighborly submanifold, is asymptotically not smaller than $2kr-k$ .

Keywords

r-neighborly submanifolds euclidean space supporting hyperplane minimal dimension asymptotic bounds geometric topology

Cite

@article{arxiv.1407.7240,
  title  = {On $r$-neighborly submanifolds in $R^N$},
  author = {Victor A. Vassiliev},
  journal= {arXiv preprint arXiv:1407.7240},
  year   = {2014}
}

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