Tilings of amenable groups
2019 ◽
Vol 2019
(747)
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pp. 277-298
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Keyword(s):
Abstract We prove that for any infinite countable amenable group G, any {\varepsilon>0} and any finite subset {K\subset G} , there exists a tiling (partition of G into finite “tiles” using only finitely many “shapes”), where all the tiles are {(K,\varepsilon)} -invariant. Moreover, our tiling has topological entropy zero (i.e., subexponential complexity of patterns). As an application, we construct a free action of G (in the sense that the mappings, associated to elements of G other than the unit, have no fixed points) on a zero-dimensional space, such that the topological entropy of this action is zero.
Keyword(s):
2017 ◽
Vol 61
(5)
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pp. 869-880
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2001 ◽
Vol 44
(2)
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pp. 231-241
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Keyword(s):
2008 ◽
Vol 28
(1)
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pp. 87-124
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2020 ◽
Vol 2020
(766)
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pp. 45-60
2020 ◽
Vol 30
(02)
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pp. 2050032
2011 ◽
Vol 32
(2)
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pp. 427-466
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Keyword(s):
2013 ◽
Vol 65
(5)
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pp. 1005-1019
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