We provide negative answers to questions posed by Durham, Hagen and Sisto on the existence of boundary maps for some hierarchically hyperbolic spaces, namely maps from right-angled Artin groups to mapping class groups. We also prove results on existence of boundary maps for free subgroups of mapping class groups.
"Nonexistence of boundary maps for some hierarchically hyperbolic spaces." Algebr. Geom. Topol. 18 (1) 409 - 439, 2018. https://doi.org/10.2140/agt.2018.18.409