Soul neighborhood conjecture for Alexandrov manifolds

Let XX be a complete open Alexandrov space with nonnegative curvature, and suppose that XX is a topological manifold. Let SS be a soul of XX.

Soul neighborhood conjecture. The space XX is homeomorphic to a small neighborhood of SS that has the structure of an open disk bundle over SS.

This is described as the topological version of the preceding soul bundle conjecture. The supplied text does not state whether this formulation is resolved independently, so its database status remains open.

Sources & referencesView supporting material

Primary source

Takao Yamaguchi, “Collapsing 4-manifolds under a lower curvature bound”, arXiv:1205.0323 (2024).

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