We provide partial results towards a conjectural generalization of a theorem of Lubotzky-Mozes-Raghunathan for arithmetic groups (over number fields or function fields) that implies, in low dimensions, both polynomial isoperimetric inequalities and finiteness properties. As a tool in our proof, we establish polynomial isoperimetric inequalities and finiteness properties for certain solvable groups that appear as subgroups of parabolic groups in semisimple groups, thus generalizing a theorem of Bux. We also develop a precise version of reduction theory for arithmetic groups whose proof is, for the most part, independent of whether the underlying global field is a number field or a function field.
Cite this article
Mladen Bestvina, Kevin Wortman, Alex Eskin, Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups. J. Eur. Math. Soc. 15 (2013), no. 6, pp. 2165–2195DOI 10.4171/JEMS/419