2 problems

Let $Y_1$ be a cobordism from $\Sigma_1$ to $\Sigma_2$ and $Y_2$ a cobordism from $\Sigma_2$ to $\Sigma_3$, with adapted harmonic Morse functions, compatible…

Let $X,Y\in \text{Alex}^n(\kappa)$ be Alexandrov spaces with non-empty boundary, and let $f:\partial X\to\partial Y$ be a homeomorphism. If the gluing $X\cup_fY$ is an Alexandrov s…