# Sharafutdinov's retraction for Alexandrov spaces.

The Sharafutdinov's retraction is defined for Open Manifolds of Nonnegative Curvature, for example in $\S 3.4$ of the book "Metric Foliations and Curvature" by Gromoll and Walschap.

For Alexandrov spaces, Perelman gave a constraction in $\S 6$ of his preprint "ALEXANDROV'S SPACES WITH CURVATURES BOUNDED FROM BELOW II". But the construction is not "that" rigous compare with the one given by Gromoll and Walschap. He definitly is a great mathematician, but I just want to make sure this is a correct construction. So are therey any published paper or more detailed construction available?

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The same construction works; I do not see any difference. –  Anton Petrunin Sep 30 '12 at 22:53
Does the Sharafutdinov retraction is unique? Which is unique for smooth case, but the proof involves exponation map. –  user3922 Oct 1 '12 at 9:51
MG: you may find http:.//wwwmath.uni-muenster.de/u/awoer_01/files/diss_woerner.pdf useful. –  Igor Belegradek Oct 1 '12 at 14:33
MG: as Anton said, Sharafutdinov's construction carries over without change. Of course, this does not mean that Perelman's proof of the soul conjecture carries over. Before asking further questions, I suggest you glance through Woerner's thesis in the link above. –  Igor Belegradek Oct 1 '12 at 17:23