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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 $3$-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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Jian Ge
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556

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.