Cockcroft Properties of Thompson’s Group
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Published:2000-09-01
Issue:3
Volume:43
Page:268-281
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ISSN:0008-4395
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Container-title:Canadian Mathematical Bulletin
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language:en
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Short-container-title:Can. math. bull.
Author:
Bogley W. A.,Gilbert N. D.,Howie James
Abstract
AbstractIn a study of the word problem for groups, R. J. Thompson considered a certain group F of self-homeomorphisms of the Cantor set and showed, among other things, that F is finitely presented. Using results of K. S. Brown and R. Geoghegan, M. N. Dyer showed that F is the fundamental group of a finite two-complex Z2 having Euler characteristic one and which is Cockcroft, in the sense that each map of the two-sphere into Z2 is homologically trivial. We show that no proper covering complex of Z2 is Cockcroft. A general result on Cockcroft properties implies that no proper regular covering complex of any finite two-complex with fundamental group F is Cockcroft.
Publisher
Canadian Mathematical Society
Subject
General Mathematics