Athiest, can a 4-D topological sphere have two or more inequivalent smooth structures?

In four dimensions there exists an uncountable family of pairwise non-diffeomorphic differentiable structures for a topological 4d sphere. This is intuitively obvious to most of us atheists of course.

Its funny, just yesterday I just happened to be reading Hendryk Pfeiffer's famous paper: "Quantum general relativity and the classification of smooth manifolds" which you will find on the bookshelves of most of us atheists. This paper directly answers this question.

Check Theorem 4.1 on page 16 of this paper for a more detailed answer to your question.

The issue of classification of smooth manifolds in quantum general relativity arises from time to time in discussions with Christians on this site who often claim the bible proves the earth is flat.

For lower dimensions, topological manifold coincide with differentiable ones - i.e. the toplogy to diff relation is 1:1. For higher dimension the two concepts go their separate ways, and a toplological manifold in general has no differential smooth structure. So it is only in 4 than we can have a "gauge invariance" of differentiability on a topological manifold or 2 or more smooth structures.

A. The Earth is not a sphere. It's actually more of an oblong-egg sort of shape. B. China is not on the "bottom" of the Earth, nor is the U.S. on the "top". Those places are called the North and South Poles. ***Special Note: I know you're a troll and this is not a sincere question. But I'm playing along anyway.

a sphere propagated into the dimension of time would take on the appearance (3 dimensionally of course) of a cylinder of radius the same as the sphere. Taking a chord of the cylinder would give us two non equivalent 4 dimensional structures. Taking a radii as the cord would give us two equivelent smooth structures. so yes, it is possible.

Yes, but only if the smooth 44-D inequivalent or lopsided hemispheres have nipple rings.

Sorry, bad day.

A sphere is a shape that's only defined in 3 dimensions. It's like asking if a triangle can have sides with equal area.

just because we're smart enough to know that there is no god doesn't mean we're all Spock from Star Trek. Of course since a 5 year old can figure out god is make believe ( my nephew did it without any help from anyone) that should go w/o saying.

I think it is still unproven but I may not be up to date with such things. So if you have proved it congratulations. A million dollars buys a lot of carrots.

only if inverted through a hypersphere on the preceding wednesday

Em yeah, of course.

Why ask a question that the answer is so well known to anyone who has any understanding of physics?