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/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

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

Zendy Tools

Zendy Open

Sofic groups generalise both residually finite and amenable groups, and theconcept is central to many important results and conjectures in measured grouptheory. We introduce a topological notion of a sofic boundary attached to agiven sofic approximation of a finitely generated group and use it to provethat coarse properties of the approximation (property A, asymptotic coarseembeddability into Hilbert space, geometric property (T)) imply correspondinganalytic properties of the group (amenability, a-T-menability and property(T)), thus generalising ideas and results present in the literature forresidually finite groups and their box spaces. Moreover, we generalise coarserigidity results for box spaces due to Kajal Das, proving that coarselyequivalent sofic approximations of two groups give rise to a uniform measureequivalence between those groups. Along the way, we bring to light a coarsegeometric view point on ultralimits of a sequence of finite graphs firstexposed by Jan \v{S}pakula and Rufus Willett, as well as proving some bridgingresults concerning measure structures on topological groupoid Moritaequivalences that will be of interest to groupoid specialists.

Sofic boundaries of groups and coarse geometry of sofic approximations