(July 16, 2012 at 2:14 pm)CliveStaples Wrote: The torus would be topologically distinguishable from a sphere--any loop enclosing the hole could not be shrunk to a point while remaining on the torus, whereas every loop on a sphere can be shrunk to a point.
If they're topologically distinguishable, then they will be geometrically distinguishable (since geometric manifolds incorporate topological manifolds).
Is the same true for a sphere enclosing a sphere? At what point does the surface of the object become the object?