On the Asymptotic and Continuous Orlicz Cohomology of Locally Compact Groups

Asymptotic $L^p$-cohomology was introduced by Pansu in 1995; it is constructed from a metric measure space with bounded geometry. Pansu proved that asymptotic $L^p$-cohomology is a quasi-isometry invariant. In 2020, Bourdon and Remy showed that if $G$ is a locally compact second countable topological group equipped with a left-invariant proper metric then its asymptotic and continuous $L_p$-cohomologies are isomorphic. We consider the Orlicz space analogs of these cohomologies and establish the Orlicz versions of the above-mentioned results.
(This is a joint work with Emiliano Sequeira)