Randomized trial characterizes braid group actions on ℝ, revealing implications for mapping class groups.
Key Points
This research aims to characterize the actions of the braid group on ℝ that produce translation numbers consistent with the standard Nielsen–Thurston action.
Characterization of braid group actions on ℝ using homeomorphisms.
Proof of analogous statements regarding left orderings of the braid group.
Examination of isolated points in the space of left orderings and conjugacy action.
Identified conditions under which braid group actions yield equivalent translation numbers as the Nielsen–Thurston action.
Extended rigidity results regarding mapping class group actions to low-genus surfaces with marked points.