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PreprintarXiv licencearXiv

Hyperpolarity of polar foliations of codimension two

Abstract

We consider polar foliations of codimension two on compact simply connected irreducible symmetric spaces. In rank at least two, we prove that these foliations are hyperpolar, settling the remaining case of the hyperpolarity problem discussed by Lytchak. We show that, for irreducible spherical Coxeter quotients, the horizontal universal cover fails to be a spherical building precisely on the Cayley plane, where every such foliation is congruent to one of the two known homogeneous models.

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BibTeX
@misc{wiesendorf2026hyperpolarity,
  title = {{Hyperpolarity of polar foliations of codimension two}},
  author = {Stephan Wiesendorf},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08480},
  eprint = {2611.08480},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08480},
}
RIS
TY  - UNPB
TI  - Hyperpolarity of polar foliations of codimension two
AU  - Stephan Wiesendorf
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.08480
UR  - https://arxiv.org/abs/2611.08480
AB  - We consider polar foliations of codimension two on compact simply connected irreducible symmetric spaces. In rank at least two, we prove that these foliations are hyperpolar, settling the remaining case of the hyperpolarity problem discussed by Lytchak. We show that, for irreducible spherical Coxeter quotients, the horizontal universal cover fails to be a spherical building precisely on the Cayley plane, where every such foliation is congruent to one of the two known homogeneous models.
ER  -