On three-dimensional Alexandrov spaces

@article{GalazGarca2013OnTA,
  title={On three-dimensional Alexandrov spaces},
  author={Fernando Galaz‐Garc{\'i}a and Luis Guijarro},
  journal={arXiv: Differential Geometry},
  year={2013}
}
We study three-dimensional Alexandrov spaces with a lower curvature bound, focusing on extending three classical results on three-dimensional manifolds: First, we show that a closed three-dimensional Alexandrov space of positive curvature, with at least one topological singularity, must be homeomorphic to the suspension of the real projective plane; we use this to classify, up to homeomorphism, closed, positively curved Alexandrov spaces of dimension three. Second, we classify closed three… 

Three-Dimensional Alexandrov Spaces with Positive or Nonnegative Ricci Curvature

We study closed three-dimensional Alexandrov spaces with a lower Ricci curvature bound in the CD∗(K,N) sense, focusing our attention on those with positive or nonnegative Ricci curvature. First, we

Cohomogeneity one Alexandrov spaces in low dimensions

Alexandrov spaces are complete length spaces with a lower curvature bound in the triangle comparison sense. When they are equipped with an effective isometric action of a compact Lie group with

Cohomogeneity one Alexandrov spaces in low dimensions

Alexandrov spaces are complete length spaces with a lower curvature bound in the triangle comparison sense. When they are equipped with an effective isometric action of a compact Lie group with

Rigidity of actions on metric spaces close to three dimensional manifolds

. In this paper we propose a metric variation on the C 0 version of the Zimmer program for three manifolds. After a reexami-nation of the isometry groups of geometric three-manifolds, we consider

Finiteness and realization theorems for Alexandrov spaces with bounded curvature

Every closed Alexandrov space with a lower and upper curvature bound (in the triangle comparison sense) is a space of bounded curvature (in the sense of Berestovskii and Nikolaev). These spaces are

Three-Dimensional Alexandrov Spaces with Positive or Nonnegative Ricci Curvature

We study closed three-dimensional Alexandrov spaces with a lower Ricci curvature bound in the CD∗(K,N) sense, focusing our attention on those with positive or nonnegative Ricci curvature. First, we

Orientability and fundamental classes of Alexandrov spaces with applications

In the present paper, we consider several valid notions of orientability of Alexandov spaces and prove that all such conditions are equivalent. Further, we give topological and geometric applications

Three-dimensional Alexandrov spaces with local isometric circle actions

We obtain a topological and equivariant classification of closed, connected three-dimensional Alexandrov spaces admitting a local isometric circle action. We show, in particular, that such spaces are

Alexandrov spaces with maximal radius

Abstract. In this paper we prove several rigidity theorems related to and including Lytchak's problem. The focus is on Alexandrov spaces with \curv\geq1, nonempty boundary, and maximal radius

Riemannian Orbifolds with Non-Negative Curvature

RIEMANNIAN ORBIFOLDS WITH NON-NEGATIVE CURVATURE Dmytro Yeroshkin Wolfgang Ziller Recent years have seen an increase in the study of orbifolds in connection to Riemannian geometry. We connect this

References

SHOWING 1-10 OF 44 REFERENCES

On the structure of manifolds with positive scalar curvature

Publisher Summary This chapter discusses some recent results by Richard Schoen and Shing-Tung Yau on the structure of manifolds with positive scalar curvature. The chapter presents theorems which are

The geometries of 3-manifolds

The theory of 3-manifolds has been revolutionised in the last few years by work of Thurston [66-70]. He has shown that geometry has an important role to play in the theory in addition to the use of

Finite group actions on 3-manifolds

If G is a finite group acting smoothly on a closed surface F, it is well known that G leaves invariant some Riemannian metric of constant curvature on F. Thus any action of G on the 2-sphere S 2 is

The Compact 3-Manifolds Covered by S 2 × R 1

The classification of all free actions by a finite group on S2 x S1 follows from the observation that there exist only four compact 3manifolds which have S2 x R 1 for a universal covering space.

A knot characterization and 1-connected nonnegatively curved 4-manifolds with circle symmetry

We classify nonnegatively curved simply connected 4-manifolds with circle symmetry up to equivariant diffeomorphisms. The main problem is rule out knotted curves in the singular set of the orbit

A.D. Alexandrov spaces with curvature bounded below

CONTENTS § 1. Introduction § 2. Basic concepts § 3. Globalization theorem § 4. Natural constructions § 5. Burst points § 6. Dimension § 7. The tangent cone and the space of directions. Conventions

Amenable category of three–manifolds

A closed topological n-manifold M is of ame–category ≤ k if it can be covered by k open subsets such that for each path-component W of the subsets the image of its fundamental group π1(W ) → π1(M) is

Geometrization of Three-Dimensional Orbifolds via Ricci Flow

A three-dimensional closed orientable orbifold (with no bad suborbifolds) is known to have a geometric decomposition from work of Perelman along with earlier work of Boileau-Leeb-Porti and

involutions on lens spaces and other 3-manifolds

Let h be an involution of a 3-dimensional lens space L=L(p, q). h is called sense preserving if h induces the identity of H1(L). The purpose of this paper is to classify the orientation preserving PL