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Session 32. Set Theory
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Towards the universal minimal flow of the homeomorphism group of the Lelek fan |
Aleksandra Kwiatkowska, University of California, Los Angeles, USA
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The talk is based on the joint work with Dana Bartošová
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The Lelek fan is the unique up to homeomorphism compact and connected subspace of the cone over the Cantor set that has a dense set of endpoints. I will report on a work in pogress towards describing the universal minimal flow of the homeomorphism group of the Lelek fan. The key components are a generalization to multiple operations of a finite version of the Gowers' Ramsey theorem and
a dualization to the projective setting of the Kechris-Pestov-Todorcevic theory.
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