4 papers
MCS Spaces are CS
Mohammad Alattar, Lewis Tadman
In this paper we further develop the theory of MCS spaces. Our main result shows that MCS spaces, as defined by Perelman, are CS sets with respect to their MCS stratification, and…
Deformations of Lipschitz Homeomorphisms
Mohammad Alattar
We obtain the Lipschitz analogues of the results Perelman used from Siebenmann's deformation of homeomorphism theory in his proof of the stability theorem. Consequently, we obtain…
Stability and Finiteness of Wasserstein Spaces
Mohammad Alattar
Under Gromov--Hausdorff convergence, and equivariant Gromov--Hausdorff convergence, we prove stability results of Wasserstein spaces over certain classes of singular and non-singul…
Stability and equivariant Gromov--Hausdorff convergence
Mohammad Alattar
We give applications of equivariant Gromov--Hausdorff convergence in various contexts. Namely, using equivariant Gromov--Hausdorff convergence, we prove a stability result in the s…