The Fenchel-Nielsen twist in terms of the cross ratio
Takeru Asaka
TL;DR
This paper presents a method to compute the Fenchel-Nielsen twist in the enhanced Teichmüller space using cross ratio coordinates, providing a new perspective on geometric transformations.
Contribution
It introduces a novel calculation of the Fenchel-Nielsen twist directly in terms of cross ratio coordinates within the enhanced Teichmüller space.
Findings
Explicit formula for Fenchel-Nielsen twist in cross ratio coordinates
Enhanced understanding of Teichmüller space transformations
Potential applications in geometric topology
Abstract
We calculate the Fenchel-Nielsen twist in the enhanced Teichm\"uller space of a marked surface by the cross ratio coordinates.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematics and Applications · Geometric Analysis and Curvature Flows