PreprintCC0arXiv
Braid spaces have no geodesic loops
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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BibTeX
@misc{panov2026braid,
title = {{Braid spaces have no geodesic loops}},
author = {Dmitri Panov and Anton Petrunin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27437},
eprint = {2610.27437},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27437},
note = {CC0},
}
RIS
TY - UNPB
TI - Braid spaces have no geodesic loops
AU - Dmitri Panov
AU - Anton Petrunin
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27437
UR - https://arxiv.org/abs/2610.27437
AB - 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).
ER -