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The remark about Milnor's exotic spheres doesn't make any sense! Obviously, they are not aspherical! Are there any examples of fake smooth structures on compact aspherical manifolds?
Also, why does the statement of the space form conjecture speak of Riemannian manifolds? The metric seems to have no bearing on the question.
This perplexes me as well. In other words, it would be nice if someone explains the relation between the space form conjecture and space forms. Oded (talk) 15:18, 21 April 2008 (UTC)
I am not a topologist. However here is an answer from a topologist I consulted regarding to the first question: "It would be wrong to think that the diffeomorphism type is unique – tori connected sum Milnor spheres gives a counterexample. ( I think this is what the author was trying to say.)". Oded (talk) 15:18, 21 April 2008 (UTC)