PreprintarXiv licencearXiv
Self-intersecting sections of polar actions on simply connected manifolds
Abstract
We construct a polar action of SU(3) on a closed simply connected $11$-manifold with a compact three-dimensional section that is not injectively immersed. The section is injective over the regular part and has two distinct local branches along a singular stratum. All isotropy groups are connected, and all orbits are simply connected. This gives a negative answer to the injectivity question raised by Grove and Ziller.
Related
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BibTeX
@misc{wiesendorf2026selfintersecting,
title = {{Self-intersecting sections of polar actions on simply connected manifolds}},
author = {Stephan Wiesendorf},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12446},
eprint = {2610.12446},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12446},
}
RIS
TY - UNPB
TI - Self-intersecting sections of polar actions on simply connected manifolds
AU - Stephan Wiesendorf
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12446
UR - https://arxiv.org/abs/2610.12446
AB - We construct a polar action of SU(3) on a closed simply connected $11$-manifold with a compact three-dimensional section that is not injectively immersed. The section is injective over the regular part and has two distinct local branches along a singular stratum. All isotropy groups are connected, and all orbits are simply connected. This gives a negative answer to the injectivity question raised by Grove and Ziller.
ER -