Converse gluing conjecture for Alexandrov spaces
Let X,Y∈Alexn(κ)X,Y\in \text{Alex}^n(\kappa)X,Y∈Alexn(κ) be Alexandrov spaces with non-empty boundary, and let f:∂X→∂Yf:\partial X\to\partial Yf:∂X→∂Y be a homeomorphism. If the gluing X∪fYX\cup_fYX∪fY is an Alexandrov s…