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math.GT2023
Strip deformations of decorated hyperbolic polygons
Pallavi Panda
In this paper we study the hyperbolic and parabolic strip deformations of ideal (possibly once-punctured) hyperbolic polygons whose vertices are decorated with horoballs. We prove…
math.GT2023
Parametrisation of decorated Margulis spacetimes using strip deformations
Pallavi Panda
Margulis spacetimes are complete affine 3-manifolds that were introduced to show that the cocompactness condition of Auslander's conjecture is necessary. There are Lorentzian manif…
math.CO2023
The arc complexes of partially decorated hyperbolic polygons
Pallavi Panda
We consider two families of hyperbolic polygons: ideal and ideal once-punctured, some of whose spikes are decorated with horoballs. We show that the arc complexes of these two fami…