Spaces of locally convex curves in S^n and combinatorics of the group B^+_{n+1}
Journal of Singularities, Tome 4 (2012), pp. 1-22
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In the 1920's Marston Morse developed what is now known as Morse theory trying to study the topology of the space of closed curves on S^2. We propose to attack a very similar problem, which 80 years later remains open, about the topology of the space of closed curves on S^2 which are locally convex (i.e., without inflection points). One of the main difficulties is the absence of the covering homotopy principle for the map sending a non-closed locally convex curve to the Frenet frame at its endpoint.
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author = {Nicolau C. Saldanha and Boris Shapiro},
title = {Spaces of locally convex curves in {S^n} and combinatorics of the group {B^+_{n+1}}},
journal = {Journal of Singularities},
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Nicolau C. Saldanha; Boris Shapiro. Spaces of locally convex curves in S^n and combinatorics of the group B^+_{n+1}. Journal of Singularities, Tome 4 (2012), pp. 1-22. doi: 10.5427/jsing.2012.4a
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