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arXiv · 2610.27437

Braid spaces have no geodesic loops

Dmitri Panov·Anton Petrunin
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Abstract

The braid spaces are defined as universal metric coverings of the standard complex spaces, branched over certain hyperplane arrangements. We describe a natural family of convex functions on braid spaces and use them to prove that braid spaces contain no geodesic loops. This statement is a consequence of the well-known conjecture that every braid space is CAT(0).

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Dmitri Panov, Anton Petrunin. 2026-10-20. Braid spaces have no geodesic loops. https://arxiv.org/abs/2610.27437

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