TY - JOUR
T1 - Amenable groups with very poor compression into Lebesgue spaces
AU - Austin, Tim
PY - 2011/8/15
Y1 - 2011/8/15
N2 - We give a construction of finitely generated amenable groups that do not admit any coarse 1-Lipschitz embedding with positive compression exponent into Lp for any 1 ≤ p < ∞, including some that are four-step solvable, answering positively a question posed by Arzhantseva, Guba, and Sapir.
AB - We give a construction of finitely generated amenable groups that do not admit any coarse 1-Lipschitz embedding with positive compression exponent into Lp for any 1 ≤ p < ∞, including some that are four-step solvable, answering positively a question posed by Arzhantseva, Guba, and Sapir.
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U2 - 10.1215/00127094-1415860
DO - 10.1215/00127094-1415860
M3 - Article
AN - SCOPUS:80051776594
SN - 0012-7094
VL - 159
SP - 187
EP - 222
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 2
ER -