Compacta and their homeomorphism groups from posets, part 2

Prelegent(ci)

Maciej Malicki

Afiliacja

IM PAN

Termin

13 grudnia 2023 16:15

Pokój

p. 5050

Seminarium

Seminarium „Topologia i teoria mnogości”

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Very recently A. Bartoš, T. Bice and A. Vignati discovered a duality, generalizing the Stone duality, between second countable T_1 compacta and graded omega-posets. Their approach allows for elementary combinatorial constructions, in the spirit of Fraïssé theory, of classical continua such as the Lelek fan or the pseudo-arc.
We extend this framework to study homeomorphism groups of compacta. We characterize Hausdorff compacta such that their group of homeomorphisms has a dense or a comeager conjugacy class. We use this characterization to prove that there exists a comeager conjugacy class in the group of homeomorphisms of the Lelek fan. This sheds light on the dynamics on the Lelek fan: a generic homeomorphism has no Lie-Yorke pair; in particular, its topological entropy is zero. We also show that there is a homeomorphism of the pseudo-arc with a dense conjugacy class.
This is an ongoing project with Tristan Bice.

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