From the 1 of 18 linked papers with an AI index.
18 papers
A torsion-free non-sofic group
Francesco Fournier-Facio
OpenAI announced the existence of a non-sofic group: the unit group of the binary Leavitt algebra. We exhibit a different source of examples (relying on the same technical criterio…
Finiteness properties and Higman's rope trick
Francesco Fournier-Facio, Matthew C. B. Zaremsky
In 1961 Higman proved that every finitely generated recursively presented group embeds into a finitely presented group. In 2018 Leary proved that every finitely generated group emb…
Bounded cohomology, quotient extensions, and hierarchical hyperbolicity
Francesco Fournier-Facio, Giorgio Mangioni, Alessandro Sisto
The authors introduce bounded central extensions (those whose Euler class is represented by a bounded cocycle) and prove that such extensions of hierarchically hyperbolic groups (H…
An improved characterisation of inner automorphisms of groups
Francesco Fournier-Facio
We show that every group embeds malnormally into a simple, complete co-Hopfian group . This implies that a non-trivial endomorphism of extends to if and only if it i…
Kazhdan groups of dimension with prescribed second -Betti number
Francesco Fournier-Facio, Roman Sauer
We construct a family of simple, lacunary hyperbolic groups with property that have rational cohomological dimension~ and whose second -Betti number can be prescr…
The Local Lifting Property, Property FD, and stability of approximate representations
Francesco Fournier-Facio, Rufus Willett
We establish Kirchberg's Local Lifting Property and Lubotzky--Shalom's Property FD for classes of finitely generated groups of central importance in geometric and combinatorial gro…