Introduces class C of groups with smooth conjugacy for minimal line actions, proves stability and inclusion of piecewise affine groups, and exhibits a finitely generated G not in C with amenability equivalent to Thompson's F.
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Circular orders admit convex uniform structures that describe their compactifications, yielding new results on G-compactifications and generalizations of Helly's selection theorem.
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Groups with classifiable actions on the line
Introduces class C of groups with smooth conjugacy for minimal line actions, proves stability and inclusion of piecewise affine groups, and exhibits a finitely generated G not in C with amenability equivalent to Thompson's F.
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Circular orders: topology and continuous actions
Circular orders admit convex uniform structures that describe their compactifications, yielding new results on G-compactifications and generalizations of Helly's selection theorem.