MathDBThe fiber representation conjecture for COMs
The fiber representation conjecture for COMs
A COM is a complex of oriented matroids, and an OM is an oriented matroid. A fiber of a COM is an intersection of its halfspaces. The conjecture is that every COM can be obtained in this way from an OM.
Fiber representation conjecture. Every COM is a fiber of some OM.
This would generalize the realizable situation and, together with the Topological Representation Theorem for oriented matroids, give a natural topological representation theorem for COMs. The source presents the claim as open.
Sources & referencesView supporting material
Primary source
Hans-Juergen Bandelt, Victor Chepoi and Kolja Knauer, “COMs: Complexes of Oriented Matroids”, arXiv:1507.06111 (2018).
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