Self-intersecting sections of polar actions on simply connected manifolds

Stephan Wiesendorf

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arXiv · 2610.12446

Self-intersecting sections of polar actions on simply connected manifolds

Stephan Wiesendorf

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Abstract

We construct a polar action of $\mathrm{SU}(3)$ 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.

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Stephan Wiesendorf. 2026-10-08. Self-intersecting sections of polar actions on simply connected manifolds. https://arxiv.org/abs/2610.12446

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