6 papers · 1 filter
Ollivier--Ricci Curvature on Groups of Polynomial Growth
Camillo Brena, Elia Bruè
We study Ollivier--Ricci curvature on Cayley graphs of groups of polynomial growth. Our main result shows that non-negative Ollivier--Ricci curvature forces the group to be virtual…
Compact Manifolds with Unbounded Nilpotent Fundamental Groups and Positive Ricci Curvature
Elia Bruè, Aaron Naber, Daniele Semola
It follows from the work of Kapovitch and Wilking that a closed manifold with nonnegative Ricci curvature has an almost nilpotent fundamental group. Leftover questions and conjectu…
Six dimensional counterexample to the Milnor Conjecture
Elia Bruè, Aaron Naber, Daniele Semola
We extend our previous work by building a smooth complete manifold with and whose fundamental group is infinitely…
Fukaya-Yamaguchi Conjecture in Dimension Four
Elia Bruè, Aaron Naber, Daniele Semola
Fukaya and Yamaguchi conjectured that if is a manifold with nonnegative sectional curvature, then the fundamental group is uniformly virtually abelian. In this short note we…
Lower Ricci Curvature Bounds and the Orientability of Spaces
Camillo Brena, Elia Bruè, Alessandro Pigati
We study orientability in spaces with Ricci curvature bounded below. Building on the theory developed by Honda, we establish equivalent characterizations of orientability for Ricci…
Topological regularity and stability of noncollapsed spaces with Ricci curvature bounded below
Elia Bruè, Alessandro Pigati, Daniele Semola
We investigate the topological regularity and stability of noncollapsed Ricci limit spaces . We confirm a conjecture proposed by Colding and Naber in di…