### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 268-281 |

Number of pages | 14 |

Journal | Canadian Mathematical Bulletin |

Volume | 43 |

Issue number | 3 |

Publication status | Published - Sep 2000 |

### Keywords

- Cockcroft two-complex
- Covering space
- Thompson's group
- Two-complex

## Fingerprint Dive into the research topics of 'Cockcroft properties of Thompson's group'. Together they form a unique fingerprint.

## Cite this

*Canadian Mathematical Bulletin*,

*43*(3), 268-281.