Relative expanders

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• 作者：Goulnara Arzhantseva ; Romain Tessera
• 关键词：Relative Kazhdan’s property (T) ; Haagerup property ; Gromov’s a ; T ; menability ; expander ; box space ; 46B85 ; 20F69 ; 22D10 ; 20E22
• 刊名：Geometric And Functional Analysis
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：25
• 期：2
• 页码：317-341
• 全文大小：365 KB
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  22. Johnson, W.B., Randrianarivony, N.L. (2006) l
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8970

文摘

We exhibit a finitely generated group G and a sequence of finite index normal subgroups such that for every finite generating subset \({S\subseteq G}\) , the sequence of finite Cayley graphs (G/N n , S) does not coarsely embed into any L p -space for \({1 \leqslant p (moreover, into any uniformly curved Banach space), and yet admits no weakly embedded expander. The reason why our examples do not coarsely embed is a new phenomenon called relative expansion, which we define in terms of Poincaré inequalities.