Kevin Wampler wrote:

> I thought the underlying assumption in this thread was that we're 
> dealing spaces equipped with a metric tensor, do you automatically get a 
> definition of distance in the standard manner.  How does this require 
> extra care to define?
> 
> I suppose you could argue that circles are a bit trickier to define, but 
> I think the normal one will work well, and should even be well-behaved 
> on genus-0 manifolds, or locally on any smooth manifold (like spherical 
> or hyperbolic spaces).

That's a whole crapload of jargon, right there.

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