Patchworking oriented matroids

Marcel Celaya, Georg Loho*, Chi Ho Yuen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In a previous work, we gave a construction of (not necessarily realisable) oriented matroids from a triangulation of a product of two simplices. In this follow-up paper, we use a combinatorial analogue of Viro's patchworking to derive a topological representation of the oriented matroid directly from the polyhedral structure of the triangulation. This provides a combinatorial manifestation of patchworking besides tropical algebraic geometry. We achieve this by defining a general homeomorphism-preserving operation on regular cell complexes which acts by merging adjacent cells in the complex together. We then rephrase the patchworking procedure in terms of this process using the theory of tropical oriented matroids.

Original languageEnglish
Pages (from-to)3545-3576
Number of pages32
JournalJournal of the London Mathematical Society
Volume106
Issue number4
DOIs
StatePublished - Dec 2022

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