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Dec 16, 2014 at 16:31 vote accept john mangual
Dec 11, 2014 at 21:14 history edited Robert Bryant CC BY-SA 3.0
deleted 4 characters in body
Dec 11, 2014 at 17:17 history edited Robert Bryant CC BY-SA 3.0
Fixed an error that led to describing the double cover of the desired object
Dec 11, 2014 at 17:03 comment added Robert Bryant @DylanThurston: Oh, yes, you are right. I always think oriented circles, but, of course, the subgroup preserving a circle need not preserve the orientation, so it's actually the quotient by the orientation-reversing involution. I'll fix the answer above.
Dec 11, 2014 at 16:38 comment added Dylan Thurston You're actually describing the double cover of the correct answer, which is also the space of oriented circles.
Dec 11, 2014 at 16:23 comment added Hao Chen We also call it "de Sitter space".
Dec 11, 2014 at 16:21 history edited Robert Bryant CC BY-SA 3.0
Added a bit more detail to the answer
Dec 11, 2014 at 16:13 history answered Robert Bryant CC BY-SA 3.0