"2D slice of a 6D Calabi-Yau manifold", and other? Mathematically what does it mean to take a "2D slice of a 6D Calabi-Yau manifold"? Part of quote taken from the top of, http://en.wikipedia.org/wiki/Calabi–Yau_manifold Is there a finite number of slices of a 6D Calabi-Yau manifold that in principle could define that Calabi-Yau manifold? How are 6D Calabi-Yau manifolds classified? Does it make sense to take some 6D Calabi-Yau manifold and distort its shape a little and still keep it the "same" topologically? Can we distort one 6D Calabi-Yau manifold into another? Does it make sense to say that there is a minimum number of "flat" complex dimensions a typical 6D Calabi-Yau manifold can be embedded? Is there a 6D Calabi-Yau manifold that could be considered most simple? What cool things "happen" when we allow for complex manifolds that don't happen for real manifolds? In string theory do the vibrating strings interact with the Calabi-Yau manifold to change the Calabi-Yau manifold even if a little bit? If some questions don't make sense, sorry, hopefully they can be modified so that they do make sense. Thanks for any help!