Arrangements of double pseudolines

Details Arrangements of double pseudolines Arrangements of double pseudolines

2011-01-05

arxiv.org/abs/1101.1022v1

Mathematics

Combinatorics

57 pages, 39 figures

Scientific paper

Define an arrangement of double pseudolines as a finite family of separating simple closed curves embedded in a real two-dimensional projective plane with the property that any two intersect in exactly four transversal intersection points and induce a cell decomposition of their underlying projective plane. We show that the dual arrangement of any finite family of pairwise disjoint convex bodies of any real two-dimensional projective geometry is an arrangement of double pseudolines and that, conversely, any arrangement of double pseudolines is isomorphic to the dual arrangement of a finite family of pairwise disjoint convex bodies of a real two-dimensional projective geometry. Furthermore we provide a simple axiomatic characterization of the class of isomorphism classes of indexed arrangements of oriented double pseudolines and we establish a one-to-one and onto correspondence between this latter class and the class of chirotopes of finite indexed families of pairwise disjoint oriented convex bodies of real two-dimensional projective geometries. Here by the chirotope of a finite indexed family of pairwise disjoint oriented convex bodies we mean the map that assigns to each triple of indices the finite set of relative positions of the convex bodies of the triple of indices with respect to each of the lines of the geometry. Similar results concerning arrangements of double pseudolines in Mobius strips and finite families of pairwise disjoint convex bodies of real two-dimensional affine geometries are reported.

Affiliated with

Also associated with

No associations

Rating

Arrangements of double pseudolines does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Arrangements of double pseudolines, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Arrangements of double pseudolines will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-267436