Arrangements of double pseudolines

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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...
Luc Habert, Michel Pocchiola
Added 13 May 2011
Updated 13 May 2011
Type Journal
Year 2011
Where CORR
Authors Luc Habert, Michel Pocchiola
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