Small product sets in compact groups
Number Theory
2016-12-06 v4 Group Theory
Abstract
We show in this paper that a sub-critical pair of sufficiently "spread-out" Borel sets in a compact and second countable group with an \emph{abelian} identity component, must reduce to a Sturmian pair in either or . This extends a classical result of Kneser.
Cite
@article{arxiv.1402.1618,
title = {Small product sets in compact groups},
author = {Michael Björklund},
journal= {arXiv preprint arXiv:1402.1618},
year = {2016}
}
Comments
24 pages, no figures. A re-write of an earlier version - significantly shorter, and (hopefully) better structured. Comments are welcome! Accepted in Fundamenta Math