Completely rewritten with an explanation of exactly why this space isn't a manifold, together with some witterings on the diffeological structure.
]]>Bleugh. Found a mistake in my argument about reparametrising curves.
]]>Started smooth structure of the path groupoid in response to Theo Something-Or-Other's question on MO. Initial input concerns the structure of the path groupoid in Euclidean space with a - perhaps surprising - conclusion.
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