Ergodicity and conullity conjectures for redundant representations
Ergodicity and conullity conjectures for redundant representations
Let be a free group, let be the group under consideration, and let be the corresponding representation space. Let be the set of redundant representations, namely representations for which some proper free factor has dense image in . Let denote the primitive-stable representations.
Redundant-representation conjecture. (a) The action of on is ergodic.
(b) is conull in .
These assertions are motivated by the contrast between proper discontinuity on Schottky and primitive-stable representations and the expected ergodic behavior on redundant representations. The excerpt does not give a resolution, so both assertions remain open.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Sources & referencesView supporting material
Primary source
Alexander Lubotzky, “Dynamics of Aut(Fn) Actions on Group Presentations and Representations”, arXiv:1109.0155 (2011).
Solutions 0
Sign in to submit a solution.
No solutions have been posted yet.