Atypical generic directions in Teichmüller space

2025/04/24 by Durham, Matthew Gentry, Wu, Chenxi, Zhu, Kejia
#20F65 #20F67 #30F60 #37E30 #37E35 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2504.17986

Abstract

Motivated by geometrically capturing generic directions in Teichmüller space -- that is, tracking rays for random walks of the mapping class group -- we use work of Chaika--Masur--Wolf and Durham--Zalloum to construct the first examples of a sublinearly-Morse Teichmüller geodesic rays with minimal non-uniquely ergodic vertical foliations.

Related

• The geometry of genericity in mapping class groups and Teichmüller spaces via CAT(0) cube complexes
• Genericity of sublinearly Morse directions in CAT(0) spaces and the Teichmüller space
• Limit sets of Teichmüller geodesics with minimal non-uniquely ergodic vertical foliation
• Divergent geodesics in the Universal Teichmüller space
• The asymptotic behavior of Teichmüller rays