On geometric flats in the {$\mathrm{CAT}(0)$} realization of Coxeter groups and Tits buildings

Pierre-Emmanuel Caprace, Frédéric Haglund

Given a complete CAT(0) space $X$ endowed with a geometric action of a group $\Gamma$, it is known that if $\Gamma$ contains a free abelian group of rank $n$, then $X$ contains a geometric f…