Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Wiesendorf, Stephan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221180774