Topological Stability and Latschev-type Reconstruction Theorems for Spaces of Curvature Bounded Above

Rafal Komendarczyk, Sushovan Majhi, Will Tran

We consider the problem of homotopy-type reconstruction of compact subsets $X\subset {\mathbb{R}}^N$ that have the Alexandrov curvature bounded above ($\le$ $\kappa$) in the intrinsic length metr…