Classification of spaces of locally convex curves in S n and combinatorics of the Weyl group D n + 1 Nicolau C . Saldanha and Boris Shapiro
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Classification of spaces of locally convex curves in S n and combinatorics of the Weyl group D n + 1 Nicolau C . Saldanha and Boris Shapiro March 22 , 2007
In 1920’s Marston Morse developed what is now known as Morse theory trying to study the topology of the space of closed curves on S2, see [7] and [5]. 80 years later a very similar problem about the topology of the space of closed and locally convex (i.e. without inflection points) curves on S2 is still widely open. The main difficulty is the absence of the covering homotopy principle for the m...
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