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Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups

Filling Bestvina, Alex Eskin, Kevin Wortman (2013)

Journal of the European Mathematical Society

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....

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