Thurston spine in a Teichmüller curve

2025/09/29 by Gao, Yue, Wang, Zhongzi
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2509.24141

Abstract

To study the Thurston spine P_g ⊆ T_g, we construct a Teichmüller curve V ⊆ T_g. Then we characterize V ∩ P_g. More specifically, we show it is a trivalent tree and is an equivariant deformation retract of V. Moreover, by our construction, a lot of essential loops in the Thurston spine, both reducible and pseudo-Anosov, are obtained.

Citations

• Small Systle Sets and Coxeter Groups
• Estimating the dimension of Thurston spine
• Hyperbolic surfaces with sublinearly many systoles that fill
• Local maxima of the systole function
• Relative shapes of thick subsets of moduli space
• Well-rounded equivariant deformation retracts of Teichmüller spaces
• Embedding surfaces into S³ with maximum symmetry
• Extremal length estimates and product regions in Teichmüller space

Related

• Estimating the dimension of Thurston spine
• An equivariant deformation retraction of the Thurston spine
• Well-rounded equivariant deformation retracts of Teichmüller spaces
• Visual sphere and Thurston's boundary of the Universal Teichm "uller\n space
• Variations of Hodge structures of a Teichmueller curve