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Article Dans Une Revue Compositio Mathematica Année : 2018

Diffeomorphism groups of tame Cantor sets and Thompson-like groups

Louis Funar

Résumé

The group of $\mathcal C^1$-diffeomorphisms of any sparse Cantor subset of a manifold is countable and discrete (possibly trivial). Thompson's groups come out of this construction when we consider central ternary Cantor subsets of an interval. Brin's higher dimensional generalizations $nV$ of Thompson's group $V$ arise when we consider products of central ternary Cantor sets. We derive that the $\mathcal C^2$-smooth mapping class group of a sparse Cantor sphere pair is a discrete countable group and produce this way versions of the braided Thompson groups.

Dates et versions

hal-01992012 , version 1 (24-01-2019)

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Louis Funar, Yurii Neretin. Diffeomorphism groups of tame Cantor sets and Thompson-like groups. Compositio Mathematica, 2018, 154 (05), pp.1066-1110. ⟨10.1112/S0010437X18007066⟩. ⟨hal-01992012⟩
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