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- FIELD
- Math:Topology
- DATE
-
Feb 27 (Tue), 2024
- TIME
- 14:00 ~ 15:30
- PLACE
- 1423
- SPEAKER
- Matte Bon, Nicolas
- HOST
- Kim, Sang-hyun
- INSTITUTE
- 리옹 대학교
- TITLE
- Laminations and structure theorems for group actions on the line (Part 2/2)
- ABSTRACT
- in-person and zoom
https://visgat.kimsh.kr
Laminations and structure theorems for group actions on the line (Part 2/2)
A lamination of the real line is a closed collection of pairwise unliked, finite intervals. They appear naturally when studying certain classes of group actions on the line. More precisely, we will discuss actions of solvable groups, and of locally moving groups (these are subgroups of Homeo(R) such that for any open interval I, the subgroups of elements fixing the complement of I acts minimally on I). A famous exampke of a locally moving group is Thompson's group F. Both classes admit "standard models" of actions on the line: solvable groups act by affine transformations, whereas locally moving groups have their defining actions. We prove a structure theorem which says that any minimal faithful action of a finitely generated group in this class is either standard, or preserves a lamination. Moreover, the large scale dynamics of actions preserving laminations can be described in terms of the standard actions. We will briefly mention the results for solvable groups, and focus the discussion on locally moving groups. This is based on works with J. Brum and C. Rivas.
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