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edit approved Jun 8, 2019 at 11:34
C.F.G
edit approved Jun 8, 2019 at 11:34
C.F.G
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This is not an answer to your question but there is a soul theorem for Alexandrov spaces due to Perelman (see Section 6 in herehere) with the conclusion that that the space deformation retracts to a soul. As Perelman explains, for Alexandrov spaces it is not true that the space is homeomorphic to a tubular neighborhood of the soul. I am not sure what happens for Alexandrov manifolds.

This is not an answer to your question but there is a soul theorem for Alexandrov spaces due to Perelman (see Section 6 in here) with the conclusion that that the space deformation retracts to a soul. As Perelman explains, for Alexandrov spaces it is not true that the space is homeomorphic to a tubular neighborhood of the soul. I am not sure what happens for Alexandrov manifolds.

This is not an answer to your question but there is a soul theorem for Alexandrov spaces due to Perelman (see Section 6 in here) with the conclusion that that the space deformation retracts to a soul. As Perelman explains, for Alexandrov spaces it is not true that the space is homeomorphic to a tubular neighborhood of the soul. I am not sure what happens for Alexandrov manifolds.

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Igor Belegradek
Igor Belegradek
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This is not an answer to your question but there is a soul theorem for Alexandrov spaces due to Perelman (see Section 6 in here) with the conclusion that that the space deformation retracts to a soul. As Perelman explains, for Alexandrov spaces it is not true that the space is homeomorphic to a tubular neighborhood of the soul. I am not sure what happens for Alexandrov manifolds.