6 papers
Flip-graphs of non-orientable filling surfaces
Pallavi Panda, Hugo Parlier, Lionel Pournin
Consider a surface with punctures that serve as marked points and at least one marked point on each boundary component. We build a filling surface by singling out one of…
Polyhedral realisations of finite arc complexes using strip deformations
François Guéritaud, Pallavi Panda
We study infinitesimal deformations of complete hyperbolic surfaces with boundary and with ideal vertices, possibly decorated with horoballs. ``Admissible'' deformations are the on…
Strong collapsibility of the arc complexes of orientable and non-orientable crowns
Pallavi Panda
We prove that the arc complex of a polygon with a marked point in its interior is a strongly collapsible combinatorial ball. We also show that the arc complex of a Möbius strip, wi…
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…
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…
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…