Fixed points in compactifications and combinatorial counterparts
Abstract
The Kechris-Pestov-Todorcevic correspondence connects extreme amenability of non-Archimedean Polish groups with Ramsey properties of classes of finite structures. The purpose of the present paper is to recast it as one of the instances of a more general construction, allowing to show that Ramsey-type statements actually appear as natural combinatorial expressions of the existence of fixed points in certain compactifications of groups, and that similar correspondences in fact exist in various dynamical contexts.
Cite
@article{arxiv.1701.04257,
title = {Fixed points in compactifications and combinatorial counterparts},
author = {Lionel Nguyen Van Thé},
journal= {arXiv preprint arXiv:1701.04257},
year = {2018}
}
Comments
32 pages; post-refereed version, with several corrections including: 1) modification of the error term in Theorems 2 and 8, 2) correction of some general statements regarding continuity of actions in introduction to section 3.3, 3) modification of proof of Proposition 20, 4) modification of proof of Proposition 21