Topology of extra space dimensions in string theory?

Question

String theory says that spacetime is really 10 dimensional and that 6 of these dimensions are curled up in a very small configuration. There is a lot of speculation as to what topology these 6 extra dimensions take. (Calabi-Yau topogologies, for example)

Why not assume that they form a 6-D hypersphere? This would be the simplest and most obvious topology. Is there some physical reason that a 6-D sphere has been ruled out?

Answer 1

11 dimensional string theory, (and 26 dimensional M theory), has not produced anything.

It is possible that the extra 7 dimensions of space in string theory, (that are not perceived), are mathematical deception that first appeared with 5 dimensional Kaluza-Klein Theory.

String theory is possibly deception involving adding dimensions of space to the already existing 3 dimensions of space one dimension at a time at 90 degree angles to the previous dimension.

That string theory is possibly invalid is stated at the end of the wikipedia article on string theory.

Answer 2

Calabi-Yau manifolds are not necessarily hyperspheres.  Why did you assume a 6-d hypershere was the "most obvious"?   We really don't know what would be most obvious...yet.