Cockcroft Properties of Thompson’s Group
Canadian mathematical bulletin, Tome 43 (2000) no. 3, pp. 268-281
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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.
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
@article{10_4153_CMB_2000_034_8,
author = {Bogley, W. A. and Gilbert, N. D. and Howie, James},
title = {Cockcroft {Properties} of {Thompson{\textquoteright}s} {Group}},
journal = {Canadian mathematical bulletin},
pages = {268--281},
year = {2000},
volume = {43},
number = {3},
doi = {10.4153/CMB-2000-034-8},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2000-034-8/}
}
TY - JOUR AU - Bogley, W. A. AU - Gilbert, N. D. AU - Howie, James TI - Cockcroft Properties of Thompson’s Group JO - Canadian mathematical bulletin PY - 2000 SP - 268 EP - 281 VL - 43 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2000-034-8/ DO - 10.4153/CMB-2000-034-8 ID - 10_4153_CMB_2000_034_8 ER -
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