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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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