Cockcroft Properties of Thompson's Group

Canadian mathematical bulletin

关键词: two-complex;    covering space;    Cockcroft two-complex;    Thompson's group;   

DOI  :  10.4153/CMB-2000-034-8

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In a study of the word problem for groups, R.~J.~Thompsonconsidered a certain group $F$ of self-homeomorphisms of the Cantorset and showed, among other things, that $F$ is finitely presented.Using results of K.~S.~Brown and R.~Geoghegan, M.~N.~Dyer showedthat $F$ is the fundamental group of a finite two-complex $Z^2$having Euler characteristic one and which is {em Cockcroft}, inthe sense that each map of the two-sphere into $Z^2$ ishomologically trivial. We show that no proper covering complex of$Z^2$ is Cockcroft. A general result on Cockcroft propertiesimplies that no proper regular covering complex of any finitetwo-complex with fundamental group $F$ is Cockcroft.

【 授权许可】

Unknown