The Barbot component B of DFR is homeomorphic to R² × [0,∞), with boundary parametrizing Pappus representations and interior extending Anosov representations from prior work via two shearing operations encoded by foliations of B.
This means that the fixed point of ρ(σ2) in X, namely the generating point p for our repre- sentation, also lies in F ′
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Patterns of Geodesics, Shearing, and Anosov Representations of the Modular Group
The Barbot component B of DFR is homeomorphic to R² × [0,∞), with boundary parametrizing Pappus representations and interior extending Anosov representations from prior work via two shearing operations encoded by foliations of B.