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Nonnegatively curved Alexandrov spaces with souls of codimension two


Author: Xueping Li
Journal: Trans. Amer. Math. Soc. 367 (2015), 3901-3928
MSC (2010): Primary 53C20, 53C99; Secondary 57N65
DOI: https://doi.org/10.1090/S0002-9947-2015-06149-2
Published electronically: February 3, 2015
MathSciNet review: 3324914
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Abstract: In this paper, we study a complete noncompact nonnegatively curved Alexandrov space $ A$ with a soul $ S$ of codimension two. We establish some structural results under additional regularity assumptions. As an application, we conclude that in this case Sharafutdinov retraction, $ \pi :\ A\to S$, is a submetry.


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Additional Information

Xueping Li
Affiliation: Department of Mathematics, Capital Normal University, Beijing, People’s Republic of China
Email: xuepingli@jsnu.edu.cn

DOI: https://doi.org/10.1090/S0002-9947-2015-06149-2
Keywords: Alexandrov space, soul, Sharafutdinov retraction, submetry, topologically nice, space of directions, join.
Received by editor(s): December 31, 2012
Published electronically: February 3, 2015
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.