单连通流形上极作用的自相交截面
Self-intersecting sections of polar actions on simply connected manifolds
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中文总结 AI 辅助
本文构造了SU(3)在闭单连通11维流形上的极作用，其紧致三维截面非单浸入，对Grove和Ziller的单射问题给出否定答案。
中文摘要 AI 辅助
我们在一个闭的单连通11维流形上构造了SU(3)的一个极作用，其紧致三维截面并非单浸入。该截面在正则部分是单射的，且在一个奇异层上有两个不同的局部分支。所有迷向群都是连通的，所有轨道都是单连通的。这对Grove和Ziller提出的单射问题给出了否定回答。
英文摘要
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.
