On compacta not admitting a stable intersection in R^n
Geometric Topology
2018-06-13 v1 General Topology
Abstract
Compacta X and Y are said to admit a stable intersection in R^n if there are maps f : X -> R^n and g : Y -> R^n such that for every sufficiently close continuous approximations f' : X -> R^n and g' : Y -> R^n of f and g we have f'(X)\cap g'(Y)\neq\emptyset. The well-known conjecture asserting that X and Y do not admit a stable intersection in R^n if and only if dim X \times Y \leq n-1 was confirmed in many cases. In this paper we prove this conjecture in all the remaining cases except the case dim X =dim Y =3, dim X \times Y=4 and n=5 which still remains open.
Cite
@article{arxiv.1310.2091,
title = {On compacta not admitting a stable intersection in R^n},
author = {Michael Levin},
journal= {arXiv preprint arXiv:1310.2091},
year = {2018}
}