English

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 (A,B)(A,B) of sufficiently "spread-out" Borel sets in a compact and second countable group KK with an \emph{abelian} identity component, must reduce to a Sturmian pair in either \bT\bT or \bT{1,1}\bT \rtimes \{-1,1\}. 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

R2 v1 2026-06-22T03:03:29.335Z