Geodesic
Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups
Journal of the European Mathematical Society, Tome 15 (2013) no. 6, pp. 2165-2195

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/jems/419
Classification : 20-XX, 22-XX
Keywords: arithmetic groups, isoperimetric inequalities 
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     title = {Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups},
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Mladen Bestvina; Alex Eskin; Kevin Wortman. Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups. Journal of the European Mathematical Society, Tome 15 (2013) no. 6, pp. 2165-2195. doi: 10.4171/jems/419

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