A family of 4-manifolds with nonnegative Ricci curvature and prescribed asymptotic cone

2024/06/04 by Shengxuan Zhou, Zhou, Shengxuan · 2 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2406.02279

Abstract

In this paper, we show that for any finite subgroup Γ< O(4) acting freely on \mathbbS³, there exists a 4-dimensional complete Riemannian manifold (M,g) with \rm Ric_g ≥ 0 , such that the asymptotic cone of (M,g) is C(\mathbbS_δ³ /Γ) for some δ= δ(Γ) >0. This answers a question of Bruè-Pigati-Semola [arXiv:2405.03839] about the topological obstructions of 4-dimensional non-collapsed tangent cones. Combining this result with a recent work of Bruè-Pigati-Semola [arXiv:2405.03839], one can classify the 4-dimensional non-collapsed tangent cone in the topological sense.

Cited by

• Ricci curvature and minimal hypersurfaces with large Betti numbers
• Instability of the fundamental group for non-collapsed Ricci-limits

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