Geodesic
Żuk’s criterion for Banach spaces and random groups
Forum of Mathematics, Sigma, Tome 11 (2023)

Voir la notice de l'article provenant de la source Cambridge University Press

We prove a Banach version of Żuk’s criterion for groups acting on partite (i.e., colorable) simplicial complexes. Using this new criterion, we derive a new fixed point theorem for random groups in the Gromov density model with respect to several classes of Banach spaces ($L^p$ spaces, Hilbertian spaces, uniformly curved spaces). In particular, we show that for every p, a group in the Gromov density model has asymptotically almost surely property $(F L^p)$ and give a sharp lower bound for the growth of the conformal dimension of the boundary of such group as a function of the parameters of the density model. 
@article{10_1017_fms_2023_80,
     author = {Izhar Oppenheim},
     title = {\.Zuk{\textquoteright}s criterion for {Banach} spaces and random groups},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {11},
     year = {2023},
     doi = {10.1017/fms.2023.80},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.80/}
}
TY  - JOUR
AU  - Izhar Oppenheim
TI  - Żuk’s criterion for Banach spaces and random groups
JO  - Forum of Mathematics, Sigma
PY  - 2023
VL  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.80/
DO  - 10.1017/fms.2023.80
LA  - en
ID  - 10_1017_fms_2023_80
ER  - 
%0 Journal Article
%A Izhar Oppenheim
%T Żuk’s criterion for Banach spaces and random groups
%J Forum of Mathematics, Sigma
%D 2023
%V 11
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.80/
%R 10.1017/fms.2023.80
%G en
%F 10_1017_fms_2023_80
Izhar Oppenheim. Żuk’s criterion for Banach spaces and random groups. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.80

Cité par Sources :