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arXiv · 2609.06247

A Counterexample to Horn's Coincidence Conjecture

Faruk Temur
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Abstract

Horn conjectured that whenever $K$ is a nonempty compact convex subset of a Banach space and $F,G:K\to K$ are continuous commuting maps, there exists $x\in K$ such that $F(x)=G(x)$. We give a counterexample in a separable Hilbert space. The construction uses an exactly commuting ladder of coincidence-free maps between finite trees, due to Oversteegen and Rogers.

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Faruk Temur. 2026-09-05. A Counterexample to Horn's Coincidence Conjecture. https://arxiv.org/abs/2609.06247

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