Abstract:
An approach to a classification of groups of line and circle homeomorphisms is discussed, based on chains of inclusions and correspondences of group classes which are induced by various characteristics of the groups.
Bibliography: 60 titles.
Keywords:
groups of line (circle) homeomorphisms, projectively invariant measures, amenability, free subgroups, growth of a group.
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 12-01-00768-a) and the programme "Leading Scientific Schools" (grant no. НШ-5998.2012.1).
Citation:
L. A. Beklaryan, “Groups of line and circle homeomorphisms. Metric invariants and questions of classification”, Russian Math. Surveys, 70:2 (2015), 203–248
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\by L.~A.~Beklaryan
\paper Groups of line and circle homeomorphisms. Metric invariants and questions of classification
\jour Russian Math. Surveys
\yr 2015
\vol 70
\issue 2
\pages 203--248
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Linking options:
https://www.mathnet.ru/eng/rm9654
https://doi.org/10.1070/RM2015v070n02ABEH004946
https://www.mathnet.ru/eng/rm/v70/i2/p3
This publication is cited in the following 2 articles:
L. A. Beklaryan, “Groups of line and circle homeomorphisms. Criteria for almost nilpotency”, Sb. Math., 210:4 (2019), 495–507
L. A. Beklaryan, “Groups of line and circle diffeomorphisms. Criteria for almost nilpotency and structure theorems”, Sb. Math., 207:8 (2016), 1079–1099
Citation in format AMSBIB
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