A topological space associated to corank 1 tropical phased matroids
Ulysses Alvarez

TL;DR
This paper extends the Folkman-Lawrence topological representation theorem to tropical phased matroids, showing that their associated topological order complex is homeomorphic to a sphere of dimension 2n-3.
Contribution
It introduces a topological space associated with tropical phased matroids and proves a sphere homeomorphism analogous to classical oriented matroids.
Findings
Topological order complex for tropical phased matroids is homeomorphic to a (2n-3)-sphere.
Establishes a new topological representation theorem for tropical phased matroids.
Connects tropical geometry with topological combinatorics.
Abstract
A consequence of the Folkman-Lawrence topological representation theorem is that the geometric realization of the order complex of the poset of non-zero covectors of a loopless rank oriented matroid on is homeomorphic to an -sphere. In this paper, we begin the study of an analogous theorem for tropical phased matroids by proving that the topological order complex for a loopless rank tropical phased matroid on is homeomorphic to a -sphere.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsPolynomial and algebraic computation · Data Management and Algorithms
