English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Coboundary expansion (with $\mathbb{F}_2$ coefficients), and variations onit, have been the focus of intensive research in the last two decades. It wasused to study random complexes, property testing, and above all Gromov'stopological overlapping property.  In part I of this paper, we extended the notion of coboundary expansion (andits variations) to cochains with permutation coefficients, equipped with thenormalized Hamming distance. We showed that this gives a unified language forstudying covering stability of complexes, as well as stability of grouphomomorphisms -- a topic that drew a lot of attention in recent years.  In this part, we extend the theory to the permutation coefficients setting.This gives some new results, even for $\mathbb{F}_2$ coefficients, opensseveral new directions of research, and suggests a pattern to proving theexistence of non-sofic groups.  Along the way, we solve the dimension $2$ case of a problem of Gromov,exhibiting a family of bounded degree coboundary expanders with $\mathbb{F}_2$coefficients.

Stability of Homomorphisms, Coverings and Cocycles II: Examples, Applications and Open problems