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We show that arithmetic subgroups of semisimple groups of relative $${{\mathbb Q}}$$-type A  n , B  n , C  n , D  n , E 6, or E 7 have an exponential lower bound to their isoperimetric inequality in the dimension that is 1 less than the real rank of the semisimple group.

Exponential higher dimensional isoperimetric inequalities for some arithmetic groups