Soul Theorem for 4-dimensional Topologically Regular Open Nonnegatively Curved Alexandrov Spaces
Differential Geometry
2010-10-12 v1
Abstract
In this paper, we study the topology of topologically regular 4-dimensional open non-negatively curved Alexandrov spaces. These spaces occur naturally as the blow-up limits of compact Riemannian manifolds with lower curvature bound. These manifolds have also been studied by Yamaguchi in his preprint [Yam2002]. Our main tools are gradient flows of semi-concave functions and critical point theory for distance functions, which have been used to study the 3-dimensional collapsing theory in the paper [CaoG2010]. The results of this paper will be used in our future studies of collapsing 4-manifolds, which will be discussed elsewhere.
Keywords
Cite
@article{arxiv.1010.1863,
title = {Soul Theorem for 4-dimensional Topologically Regular Open Nonnegatively Curved Alexandrov Spaces},
author = {Jian Ge},
journal= {arXiv preprint arXiv:1010.1863},
year = {2010}
}
Comments
11 pages, 3 figures. Accepted by Proc AMS