Soul theorem for 4-dimensional topologically regular open nonnegatively curved Alexandrov spaces

Author:
Jian Ge

Journal:
Proc. Amer. Math. Soc. **139** (2011), 4435-4443

MSC (2010):
Primary 53C20

Published electronically:
April 13, 2011

MathSciNet review:
2823089

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Abstract: In this paper, we study the topology of topologically regular 4-dimensional open nonnegatively 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. Our main tools are gradient flows of semi-concave functions and critical point theory for distance functions, which have been used to study the -dimensional collapsing theory in the paper by Cao and Ge. The results of this paper will be used in our future studies of collapsing 4-manifolds, which will be discussed elsewhere.

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Additional Information

**Jian Ge**

Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556

Email:
jge@nd.edu

DOI:
https://doi.org/10.1090/S0002-9939-2011-10831-1

Received by editor(s):
September 27, 2010

Received by editor(s) in revised form:
October 8, 2010

Published electronically:
April 13, 2011

Communicated by:
Jianguo Cao

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.