BIRS Workshop Lecture Videos
Polish dendrites & Polish groups Duchesne, Bruno
A dendrite is a continuum (i.e. a compact connected metrizable space) that is locally connected and such that any two points are joined by a unique arc. T. Wazewski introduced a universal dendrite in which any other dendrite can embedded. Its construction can be generalized to yield an uncountable family of non-homeomorphic dendrites. Their homeomorphism groups are closed subgroups of $S_\infty$ and thus are Polish groups. Moreover some of them are oligomorphic. In this talk, we will be interested in structural and topological properties of these groups like simplicity, Bergman property, property $(T)$, existence of a dense or comeager conjugacy class, automatic continuity or small index property.
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