We obtain results about fundamental groups of RCD∗⁢(K, N) spaces previously known
under additional conditions such as smoothness or lower sectional curvature bounds. For …

Gromov proved that sequences of Riemannian manifolds with nonnegative sectional
curvature have subsequences which converge in the Gromov-Hausdor sense to Alexandrov …

We prove an upper bound on the rank of the abelianised revised fundamental group (called
“revised first Betti number”) of a compact RCD. K; N/space, in the same spirit of the …

We study notions of persistent homotopy groups of compact metric spaces together with their
stability properties in the Gromov-Hausdorff sense. We pay particular attention to the case of …

We generalize and strengthen the theorem of Gromov that the fundamental group of any
compact Riemannian manifold of diameter at most D has a set of generators g1,…, gk of …

One of the most powerful theorems in metric geometry is the Arzela–Ascoli Theorem which
provides a continuous limit for sequences of equicontinuous functions between two compact …

This is an intuitive survey of extrinsic and intrinsic notions of convergence of manifolds
complete with pictures of key examples and a discussion of the properties associated with …

Geodesic currents have been a prominent tool in Geometric Topology and Teichmüller
Theory since their introduction in 1988 by Bonahon ([Bon88]). Every geodesic current on a …

Sunada's method for constructing isospectral manifolds, introduced in 1985, remains the
most widely used and cited technique. In this exposition, we gather together many of the …

arXiv:2308.15215v1 [math.DG] 29 Aug 2023 Page 1 arXiv:2308.15215v1 [math.DG] 29 Aug
2023 MARGULIS LEMMA ON RCD(K,N) SPACES QIN DENG, JAIME SANTOS-RODRÍGUEZ …