TL;DR
This paper explores the duality between two approaches to mapping class group-equivariant deformation retractions of Teichmüller space, highlighting their conceptual connections and differences.
Contribution
It demonstrates the duality between Schmutz Schaller's and Thurston's methods for deformation retractions in Teichmüller space.
Findings
Identifies the dual nature of the two approaches
Clarifies the conceptual relationship between the methods
Provides a unified perspective on deformation retractions
Abstract
Two people who pioneered the study of mapping class group-equivariant deformation retractions of Teichm\"uller space of closed compact surfaces are Schmutz Schaller and Thurston. This paper studies how the two different approaches are dual to each other.
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