00:00:00 / 00:00:00

On actions on the real line of some finitely generated groups

By Nicolás Matte Bon

Appears in collection : Big Mapping Class Groups and Diffeomorphism Groups / Gros groupes modulaires et groupes de difféomorphismes

It is well-known that a finitely generated group acts faithfully on the real line if and only if it is left-orderable. When this is the case, it is natural to study the possible representations of G into the group of homeomorphisms the real line. Several questions can be asked: how many dynamically distinct representations does G admit, and is there a 'nice' invariant that distinguishes such representations under (semi-)conjugacy? Which such representations can be conjugated into the group of diffeomorphisms (of a given regularity C^r)? Which such representations are rigid under perturbations, or when can two representations be deformed into one another by a continuous path? An object of great help in addressing such questions is the Deroin space of the group G, which is a compact space endowed with a flow which encodes all possible actions of G on the line (whose construction is based on work of Deroin-Kleptsyn-Navas-Parwani). Which I will survey some results that address these questions for various groups, including finitely generated solvable groups and a class of groups which includes Thompson's group F. The talk is based on joint works with J. Brum, C. Rivas and M. Triestino.

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.19968403
  • Cite this video Matte Bon Nicolás (10/13/22). On actions on the real line of some finitely generated groups. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19968403
  • URL https://dx.doi.org/10.24350/CIRM.V.19968403

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow




Register

  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
    community
  • Get notification updates
    for your favorite subjects
Give feedback