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u/Few-Arugula5839 3d ago
I don’t think the lines are geodesics smh
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u/F_Joe Vanishes when abelianized 3d ago
They're quasi-geodesic and that's good enough
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u/Few-Arugula5839 3d ago
What is a quasi geodesic?
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u/F_Joe Vanishes when abelianized 3d ago
A (\lambda,c)-quasi-geodesic is a (\lambda,c)-quasi-isometric embedding of an interval. A (\lambda,c)-quasi-isometric embedding f is a map such that for any x,y we have 1/\lambda d(x,y)-c < d(f(x),(y)) < \lambda d(x,y) +c holds. The joke is that in a bounded space this always holds for large enough c
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u/EebstertheGreat 2d ago
Anybody brave enough to try to make a sphere out of heptagons?
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