Characterization of a class of convex curves on S^3 via decomposition of locally convex curves into a pair on S^2.
The space of non-degenerate closed curves in a Riemannian manifold
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abstract
Let LM be the semigroup of non-degenerate based loops with a fixed initial/final frame in a Riemannian manifold M of dimension at least three. We compare the topology of LM to that of the loop space Omega FTM on the bundle of frames in the tangent bundle of M. We show that Omega FTM is the group completion of LM, and prove that it is obtained by localizing LM with respect to adding a "small twist".
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math.GT 1years
2020 1verdicts
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Characterization of some convex curves on the 3-sphere
Characterization of a class of convex curves on S^3 via decomposition of locally convex curves into a pair on S^2.