Colorable hierarchically hyperbolic groups admit asymptotically CAT(0) metrics and Bestvina-Dranishnikov Z-structures, leading to the Farrell-Jones conjecture for extra-large type Artin groups and other new classes.
On boundaries of bicombable spaces
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abstract
We initiate systematic study of EZ-structures (and associated boundaries) of groups acting on spaces that admit consistent and conical (equivalently, consistent and convex) geodesic bicombings. Such spaces recently drew a lot of attention due to the fact that many classical groups act `nicely' on them. We rigorously construct EZ-structures, discuss their uniqueness (up to homeomorphism), provide examples, and prove some boundary-related features analogous to the ones exhibited by CAT(0) spaces and groups, which form a subclass of the discussed class of spaces and groups.
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Asymptotically CAT(0) metrics, Z-structures, and the Farrell-Jones Conjecture
Colorable hierarchically hyperbolic groups admit asymptotically CAT(0) metrics and Bestvina-Dranishnikov Z-structures, leading to the Farrell-Jones conjecture for extra-large type Artin groups and other new classes.