Year: 2026
Type: article
Abstract: In this paper, we show that, for any finite subgroup Γ < O ( 4 ) \Gamma acting freely on S 3 \mathbb{S}^{3} , there exists a 4-dimensional complete Riemannian manifold ( M , g ) (M,g) with Ric g ≥ 0 \mathrm{Ric}_{g}\geq 0 such that the asymptotic cone of ( M , g ) (M,g) is C ( S δ 3 / Γ ) C(\mathbb{S}_{\delta}^{3}/\Gamma) for some δ = δ ( Γ ) > 0 \delta=\delta(\Gamma)>0 . This answers a question of Bruè–Pigati–Semola [E. Bruè, A. Pigati and D. Semola, Topological regularity and stability of noncollapsed spaces with Ricci curvature bounded below, preprint (2024), https://arxiv.org/abs/2405.03839 ] about the topological obstructions of 4-dimensional non-collapsed tangent cones. Combining this result with the work of Bruè–Pigati–Semola, one can classify the 4-dimensional non-collapsed tangent cone in the topological sense.
Author: Shengxuan Zhou
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7130504426