Thompson's Group and the Linear Group GL_∞(Z)  

作　　者：Yan WU Xiaoman CHEN 

机构地区：[1]College of Mathematics Physics and Information Engineering, Jiaxing University, Jiaxing 314033, Zhejiang, China [2]School of Mathematical Sciences, Fudan University, Shanghai 200433, China

出　　处：《Chinese Annals of Mathematics,Series B》2011年第6期863-884,共22页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China (No. 10731020);the Shanghai Natural Science Foundation of China (No. 09ZR1402000)

摘　　要：The authors study the finite decomposition complexity of metric spaces of H, equipped with different metrics, where H is a subgroup of the linear group GL∞（E）. It is proved that there is an injective Lipschitz map φ： （F, ds） --＊ （H,d）, where F is the Thompson＇s group, ds the word-metric of F with respect to the finite generating set S and d a metric of H. But it is not a proper map. Meanwhile, it is proved that φ（F, ds） → （H, dl） is not a Lipschitz map, where dl is another metric of H.

关 键 词：Finite decomposition complexity Thompson＇s group F Word-metric Lipschitz map Reduced tree diagram 

分 类 号：O152.3[理学—数学] TP311[理学—基础数学]