Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups

Bestvina, Filling, Eskin, Alex, and Wortman, Kevin. "Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups." Journal of the European Mathematical Society 015.6 (2013): 2165-2195. <http://eudml.org/doc/277423>.

@article{Bestvina2013,
abstract = {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.},
author = {Bestvina, Filling, Eskin, Alex, Wortman, Kevin},
journal = {Journal of the European Mathematical Society},
keywords = {arithmetic groups; isoperimetric inequalities; arithmetic groups; isoperimetric inequalities},
language = {eng},
number = {6},
pages = {2165-2195},
publisher = {European Mathematical Society Publishing House},
title = {Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups},
url = {http://eudml.org/doc/277423},
volume = {015},
year = {2013},
}

TY - JOUR
AU - Bestvina, Filling
AU - Eskin, Alex
AU - Wortman, Kevin
TI - Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups
JO - Journal of the European Mathematical Society
PY - 2013
PB - European Mathematical Society Publishing House
VL - 015
IS - 6
SP - 2165
EP - 2195
AB - 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.
LA - eng
KW - arithmetic groups; isoperimetric inequalities; arithmetic groups; isoperimetric inequalities
UR - http://eudml.org/doc/277423
ER -