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In this article, we study the smooth mapping class group of a surface S relative to a given Cantor set, that is the group of isotopy classes of orientation-preserving smooth… Click to show full abstract
In this article, we study the smooth mapping class group of a surface S relative to a given Cantor set, that is the group of isotopy classes of orientation-preserving smooth diffeomorphisms of S which preserve this Cantor set. When the Cantor set is the standard ternary Cantor set, we prove that the subgroup consisting of diffeomorphisms which are isotopic to the identity on S does not contain any distorted elements. Moreover, we prove a weak Tits alternative for these groups.
Keywords:
smooth mapping;
tits alternative;
mapping class;
cantor set
Journal Title: Transactions of the American Mathematical Society
Year Published: 2019
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Journal Title: Transactions of the American Mathematical Society
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!