Groups of line and circle homeomorphisms. Criteria for almost nilpotency
Sbornik. Mathematics, Tome 210 (2019) no. 4, pp. 495-507
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For finitely-generated groups of line and circle homeomorphisms a criterion for their being almost nilpotent is established in terms of free two-generator subsemigroups and the condition of maximality. Previously the author found a criterion for almost nilpotency stated in terms of free two-generator subsemigroups for finitely generated groups of line and circle homeomorphisms that are $C^{(1)}$-smooth and mutually transversal. In addition, for groups of diffeomorphisms, structure theorems were established and a number of characteristics of such groups were proved to be typical. It was also shown that, in the space of finitely generated groups of $C^{(1)}$-diffeomorphisms with a prescribed number of generators, the set of groups with mutually transversal elements contains a countable intersection of open dense subsets (is residual). Navas has also obtained a criterion for the almost nilpotency of groups of $C^{(1+\alpha)}$-diffeomorphisms of an interval, where $\alpha>0$, in terms of free subsemigroups on two generators.
Bibliography: 21 titles.
Keywords:
almost nilpotency, group of line or circle homeomorphisms, free subsemigroup.
@article{SM_2019_210_4_a1,
author = {L. A. Beklaryan},
title = {Groups of line and circle homeomorphisms. {Criteria} for almost nilpotency},
journal = {Sbornik. Mathematics},
pages = {495--507},
publisher = {mathdoc},
volume = {210},
number = {4},
year = {2019},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2019_210_4_a1/}
}
L. A. Beklaryan. Groups of line and circle homeomorphisms. Criteria for almost nilpotency. Sbornik. Mathematics, Tome 210 (2019) no. 4, pp. 495-507. http://geodesic.mathdoc.fr/item/SM_2019_210_4_a1/