Geodesic
Acyclicity of Certain Homeomorphism Groups
Canadian journal of mathematics, Tome 42 (1990) no. 1, pp. 80-94

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

The concept of a mitotic group was introduced in [3] by Baumslag, Dyer and Heller who showed that mitotic groups were acyclic. In [8] one of the authors introduced the concept of a pseudo-mitotic group, a concept weaker than that of a mitotic group, and showed that pseudo-mitotic groups were acyclic and that the group Gn of homeomorphisms of Rn with compact support is pseudo-mitotic. In our present paper we develop techniques to prove pseudomitoticity of certain other homeomorphism groups. In [5] Kan and Thurston observed that the group of set theoretic bijections of Q with bounded support is acyclic. A natural question is to decide whether the group of homeomorphisms of Q (resp. the irrationals I ) with bounded support is acyclic or not. In the present paper we develop techniques to answer this question in the affirmative. 
Sankaran, P.; Varadarajan, K. Acyclicity of Certain Homeomorphism Groups. Canadian journal of mathematics, Tome 42 (1990) no. 1, pp. 80-94. doi: 10.4153/CJM-1990-005-0
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