Geodesic
Cockcroft Properties of Thompson’s Group
Canadian mathematical bulletin, Tome 43 (2000) no. 3, pp. 268-281

Voir la notice de l'article provenant de la source Cambridge University Press

In 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 ${{Z}^{2}}$ having Euler characteristic one and which is Cockcroft, in the sense that each map of the two-sphere into ${{Z}^{2}}$ is homologically trivial. We show that no proper covering complex of ${{Z}^{2}}$ 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.
DOI : 10.4153/CMB-2000-034-8
Mots-clés : 57M20, 20F38, 57M10, 20F34, two-complex, covering space, Cockcroft two-complex, Thompson’s group 
Bogley, W. A.; Gilbert, N. D.; Howie, James. Cockcroft Properties of Thompson’s Group. Canadian mathematical bulletin, Tome 43 (2000) no. 3, pp. 268-281. doi: 10.4153/CMB-2000-034-8
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