# positively curved Alexandrov space

I heard a conjecture "3-dim positively curved Alexandrov space is of the form S^3/J.(I cannot make sure my statement is accurate). What is the classification of n-dim positively curved Alexandrov space? And if a n-dim positively curved Alexandrov space has a totally (quasi)geodesic subset,then the classification? Maybe it's stupid to ask such a big quesiton,I just want to know what we have known about this.can someone recommend some books or papers on it?

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Did not you ask the same question already? – Anton Petrunin Aug 30 '12 at 23:09
Anton - I think the difference in the questions is between '3' and '$n$'. – HJRW Aug 31 '12 at 12:08
Oh, I did not read it to the end --- sorry. – Anton Petrunin Aug 31 '12 at 12:32