Zhuk's bridges, centralizers, and similarity
Abstract
This is the second of three papers motivated by the author's desire to understand and explain "algebraically" one aspect of Dmitriy Zhuk's proof of the CSP Dichotomy Theorem. In this paper we extend Zhuk's "bridge" construction to arbitrary meet-irreducible congruences of finite algebras in locally finite varieties with a Taylor term. We then connect bridges to centrality and similarity. In particular, we prove that Zhuk's bridges and our "similarity bridges" (defined in our first paper) convey the same information in locally finite Taylor varieties.
Cite
@article{arxiv.2503.03551,
title = {Zhuk's bridges, centralizers, and similarity},
author = {Ross Willard},
journal= {arXiv preprint arXiv:2503.03551},
year = {2026}
}
Comments
Version 2 changes: section 4 rewritten to better align with Zhuk's definition of "bridge"; "proper" and "rooted" bridges renamed "similarity" and "good" bridges respectively; "Cov" redefined; proof of Lemma 2.7 now cites the first paper arXiv:2502.20517v3. 25 pages