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Acyclicity of Certain Homeomorphism Groups

Published online by Cambridge University Press:  20 November 2018

P. Sankaran  and
K. Varadarajan
P. Sankaran
Affiliation:
University of Calgary, Calgary, Alberta
K. Varadarajan
Affiliation:
The Institute of Mathematical Sciences, Madras, India
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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 Gnof 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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 1 , 01 February 1990 , pp. 80 - 94
Copyright
Copyright © Canadian Mathematical Society 1990

References

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