Re: [math-fun] smooth torus

On Sep 2, 2009, at 7:53 AM, Andy Latto wrote:

The question was whether the sum could be a smooth torus, not a smooth manifold with boundary. So this doesn't count.

My intuition is no, but I haven't found a proof yet.

Maybe this way of stating the problem helps: Consider two smooth maps from S^1 to R^3 given by s --> x(s) t --> y(t) Question: can the map S^1 x S^1 to R^3 given by (s,t) --> x(s) + y(t) be smooth? Veit