• Corpus ID: 232306949

Some topological results of Ricci limit spaces

  title={Some topological results of Ricci limit spaces},
  author={Jiayin Pan and Jikang Wang},
We study the topology of a Ricci limit space (X, p), which is the Gromov-Hausdorff limit of a sequence of complete n-manifolds (Mi, pi) with Ric ≥ −(n− 1). Our first result shows that, if Mi has Ricci bounded covering geometry, i.e. the local Riemannian universal cover is non-collapsed, then X is semi-locally simply connected. In the process, we establish a slice theorem for isometric pseudo-group actions on a closed ball in the Ricci limit space. In the second result, we give a description of… 


OF THE DISSERTATION On the local topology of Ricci limit spaces By Jikang Wang Dissertation Director: Xiaochun Rong A Ricci limit space (X, p) is the Gromov-Hausdorff limit of a sequence of complete

Ricci Limit Spaces Are Semi-locally Simply Connected

Let (X, p) be a Ricci limit space. We show that for any ǫ > 0 and x ∈ X, there exists r < ǫ, depending on ǫ and x, so that any loop in Br(x) is contractible in Bǫ(x). In particular, X is semi-locally



Hausdorff convergence and universal covers

We prove that if Y is the Gromov-Hausdorff limit of a sequence of compact manifolds, M n i , with a uniform lower bound on Ricci curvature and a uniform upper bound on diameter, then Y has a

Regularity of Einstein manifolds and the codimension 4 conjecture

In this paper, we are concerned with the regularity of noncollapsed Riemannian manifolds (M n ;g) with bounded Ricci curvature, as well as their Gromov-Hausdor limit spaces ( M n ;dj) dGH ! (X;d),

On the structure of spaces with Ricci curvature bounded below. II

In this paper and in we study the structure of spaces Y which are pointed Gromov Hausdor limits of sequences f M i pi g of complete connected Riemannian manifolds whose Ricci curvatures have a de

Sharp Holder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications

We prove a new estimate on manifolds with a lower Ricci bound which asserts that the geometry of balls centered on a minimizing geodesic can change in at most a Holder continuous way along the

Collapsed manifolds with Ricci bounded covering geometry

We study collapsed manifolds with Ricci bounded covering geometry, i.e., Ricci curvature is bounded below and the Riemannian universal cover is non-collapsed or consists of uniform Reifenberg points.

Ricci curvature and isometric actions with scaling nonvanishing property

In the study manifolds of Ricci curvature bounded below, a stumbling obstruction is the lack of links between large-scale geometry and small-scale geometry at a fixed reference point. There have been

On the Existence of Slices for Actions of Non-Compact Lie Groups

If G is a topological group then by a G-space we mean a completely regular space X together with a fixed action of G on X. If one restricts consideration to compact Lie groups then a substantial

Universal covers for Hausdorff limits of noncompact spaces

We prove that if Y is the Gromov-Hausdorff limit of a sequence of complete manifolds, M n i , with a uniform lower bound on Ricci curvature, then Y has a universal cover.

Structure of fundamental groups of manifolds with Ricci curvature bounded below

Verifying a conjecture of Gromov we establish a generalized Margulis Lemma for manifolds with lower Ricci curvature bound. Among the various applications are finiteness results for fundamental groups

Semi-local simple connectedness of non-collapsing Ricci limit spaces

Let $X$ be a non-collapsing Ricci limit space and let $x\in X$. We show that for any $\epsilon>0$, there is $r>0$ such that every loop in $B_t(x)$ is contractible in $B_{(1+\epsilon)t}(x)$, where