Strong collapsibility of the arc complexes of orientable and non-orientable crowns

2024/02/16 by Panda, Pallavi
#Combinatorics (math.CO) #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2402.10530

Abstract

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, with finitely many marked points on its boundary, is a simplicially collapsible combinatorial ball but is not strongly collapsible.

Related

• The Structure and Singularities of Arc Complexes
• The arc complexes of partially decorated hyperbolic polygons
• Polyhedral realisations of finite arc complexes using strip deformations
• Combinatorial rigidity of arc complexes
• The collapsibility of CAT(0) square 2-complexes