Arrangements of double pseudolines

We define a double pseudoline as a simple closed curve in the open M¨obius band homotopic to the double of its core circle, and we define an arrangement of double pseudolines as a collection of double pseudolines such that every pair crosses in 4 points – the crossings being transversal – and induces a cell decomposition of the M¨obius band whose 2-dimensional cells are 2-balls, except the unbounded cell which is a 2ball minus a point. Dual arrangements of boundaries of collection of pairwise disjoint 2-dimensional closed bounded planar convex sets are examples of arrangements of double pseudolines. We show that every pair of simple arrangements of double pseudolines is connected by a sequence of triangle-switches and that every simple arrangement of double pseudolines has a representation by a configuration of pairwise disjoint disks in the plane with pseudoline double tangents. This shows in particular that any double-permutation sequence of J.E. Goodman and R. Pollack (SoC...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Luc Habert, Michel Pocchiola
• Keywords: CORR 2011, Double Pseudolines, Education, M¨obius Bands, Pseudoline Double Tangents