Gowers' Ramsey Theorem with multiple operations and dynamics of the homeomorphism group of the Lelek fan

Aleksandra Kwiatkowska; Dana Barto\v{s}ov\'a

arxiv: 1411.5134 · v3 · pith:APGOX6SUnew · submitted 2014-11-19 · 🧮 math.LO · math.CO· math.DS

Gowers' Ramsey Theorem with multiple operations and dynamics of the homeomorphism group of the Lelek fan

Dana Barto\v{s}ov\'a , Aleksandra Kwiatkowska This is my paper

classification 🧮 math.LO math.COmath.DS

keywords gowersgrouplelekmultipleoperationsramseytheoremamenable

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We generalize the finite version of Gowers' Ramsey theorem to multiple tetris-like operations and apply it to show that a group of homeomorphisms that preserve a "typical" linear order of branches of the Lelek fan, a compact connected metric space with many symmetries, is extremely amenable.

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Gowers' Ramsey Theorem with multiple operations and dynamics of the homeomorphism group of the Lelek fan

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