2015年8月
Topological full groups of one-sided shifts of finite type
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
- 巻
- 705
- 号
- 開始ページ
- 35
- 終了ページ
- 84
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1515/crelle-2013-0041
- 出版者・発行元
- WALTER DE GRUYTER GMBH
We explore the topological full group [G] of an essentially principal etale groupoid G on a Cantor set. When G is minimal, we show that [G] (and its certain normal subgroup) is a complete invariant for the isomorphism class of the etale groupoid G. Furthermore, when G is either almost finite or purely infinite, the commutator subgroup D([G]) is shown to be simple. The etale groupoid G arising from a one-sided irreducible shift of finite type is a typical example of a purely infinite minimal groupoid. For such G, [G] is thought of as a generalization of the Higman-Thompson group. We prove that [G] is of type F-infinity, and so in particular it is finitely presented. This gives us a new infinite family of finitely presented infinite simple groups. Also, the abelianization of [G] is calculated and described in terms of the homology groups of G.
- リンク情報
- ID情報
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- DOI : 10.1515/crelle-2013-0041
- ISSN : 0075-4102
- eISSN : 1435-5345
- Web of Science ID : WOS:000359196100003