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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Structural properties of dendrite groups


Authors: Bruno Duchesne and Nicolas Monod
Journal: Trans. Amer. Math. Soc. 371 (2019), 1925-1949
MSC (2010): Primary 20B27, 22F50, 54F50, 54H15
DOI: https://doi.org/10.1090/tran/7347
Published electronically: October 11, 2018
MathSciNet review: 3894039
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be the homeomorphism group of a dendrite. We study the normal subgroups of $ G$. For instance, there are uncountably many non-isomorphic such groups $ G$ that are simple groups. Moreover, these groups can be chosen so that any isometric $ G$-action on any metric space has a bounded orbit. In particular they have the fixed point property (FH).


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Additional Information

Bruno Duchesne
Affiliation: Institut Élie Cartan, Université de Lorraine, Nancy, France
Email: bruno.duchesne@univ-lorraine.fr

Nicolas Monod
Affiliation: École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
Email: nicolas.monod@epfl.ch

DOI: https://doi.org/10.1090/tran/7347
Received by editor(s): November 7, 2016
Received by editor(s) in revised form: July 21, 2017
Published electronically: October 11, 2018
Additional Notes: The first author was supported in part by French projects ANR-14-CE25-0004 GAMME and ANR-16-CE40-0022-01 AGIRA
Article copyright: © Copyright 2018 American Mathematical Society