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arXiv · 2407.02427

Fundamentals of Broken Line Convex Geometry

Juan Bosco Frías-Medina·Timothy Magee
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Abstract

We develop the fundamentals of a new theory of convex geometry -- which we call "broken line convex geometry". This is a theory of convexity where the ambient space is the rational tropicalization of a cluster variety, as opposed to an ambient vector space. In this theory, line segments are replaced by broken line segments, and we adopt the notion of convexity in [CMN21]. We state and prove broken line convex geometry versions of many standard results from usual convex geometry.

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Juan Bosco Frías-Medina, Timothy Magee. 2024-07-02. Fundamentals of Broken Line Convex Geometry. https://arxiv.org/abs/2407.02427

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