Notes on compact nilspaces
Abstract
These notes form the second part of a detailed account of the theory of nilspaces developed by Camarena and Szegedy. Here we focus on nilspaces equipped with a compact topology that is compatible with the cube structure, called compact nilspaces. The material in these notes relies on the first part of our exposition (available as arXiv:1601.03693), and it expands on the third chapter of the paper of Camarena and Szegedy, providing more detailed proofs of their results. To that end we also include several additional results that are implicit in their paper.
Keywords
Cite
@article{arxiv.1605.08940,
title = {Notes on compact nilspaces},
author = {Pablo Candela},
journal= {arXiv preprint arXiv:1605.08940},
year = {2017}
}
Comments
This version is formatted for the journal Discrete Analysis. New material has been added following comments from the referees. Additions include several examples throughout the text, and a classification result in the last subsection, involving the Heisenberg group