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Answer by user44143 for Can geodesics be acyclically directed?
No, this is not always possible.Let $M$ be the manifold shown above, i.e. an open square subset of $R^2$, with three triangles removed, four parallelograms appended, and three identifications made. We...
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Let $M$ be a length space, and let $\Pi$ be a finite set of geodesics in this space that are the unique geodesic between their endpoints. Additionally, suppose that the intersection of any two distinct...
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