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In these lectures, we will report on some properties of the space of actions of a left-orderable group on the real line. We will notably describe the almost-periodic actions, the harmonic actions and their spaces.

20F60 ; 22F50 ; 37B05 ; 37E10 ; 57R30

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Irreducible lattices in semi-simple Lie groups of higher rank are not left-orderable I'll report on the problem of the left orderability of lattices in semi-simple Lie groups, and give some insight of our joint proof with Bertrand Deroin that in rank at least two, an irreducible lattice is not left-orderable. The proof will make use of the tools developed in the minicourse of Bertrand.

20F60 ; 37B05 ; 22F50 ; 37E10 ; 57R30

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As a counterpart to Deroin's minicourse, we discuss actions of groups on the circle in the C0 setting. Here, many dynamical properties of an action can be encoded by the algebraic data of a left-invariant circular order on the group. I will highlight rigidity and flexibility phenomena among group actions, and discuss new work with C. Rivas relating these to the natural topology on the space of circular orders on a group.

58D05 ; 37E30 ; 57S05 ; 20F60

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A group is left-orderable if it admits a strict total order that is left-invariant under the group operation. The space of left-orderings of a given countable group is a well studied compact Polish space whose topological and dynamical features interact with the algebraic properties of the group. In this talk I will discuss the Borel complexity of the conjugacy equivalence relation on the spaces of left-orderings. This is joint work with Adam Clay.[-]

A group is left-orderable if it admits a strict total order that is left-invariant under the group operation. The space of left-orderings of a given countable group is a well studied compact Polish space whose topological and dynamical features interact with the algebraic properties of the group. In this talk I will discuss the Borel complexity of the conjugacy equivalence relation on the spaces of left-orderings. This is joint work with Adam ...[+]

03E15 ; 06F15 ; 20F60 ; 57K18 ; 57K30

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Documents 20F60 4 résultats

Space of actions of groups on the real line - Deroin, Bertrand (Auteur de la Conférence) | CIRM H Nouveau

Irreducible lattices in semi-simple Lie groups of higher rank are not left-orderable - Hurtado Salazar, Sebastian (Auteur de la Conférence) | CIRM H Nouveau

Orderability and groups of homeomorphisms of the circle - Mann, Kathryn (Auteur de la Conférence) | CIRM H Nouveau

The Borel complexity of the space of left-orderings - Calderoni, Filippo (Auteur de la Conférence) | CIRM H Nouveau