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Spaces of locally convex curves in S^n and combinatorics of the group B^+_{n+1}
Stockholm University, Faculty of Science, Department of Mathematics.
2012 (English)In: Journal of Singularities, ISSN 1949-2006, E-ISSN 1949-2006, Vol. 4, 1-22 p.Article in journal (Refereed) Published
Abstract [en]

In the 1920's Marston Morse developed what is now known as Morse theorytrying to study the topology of the space of closed curveson $\Ss^2$ (\cite{Morse}, \cite {Klingenberg}).We propose to attack a very similar problem,which 80 years later remains open,about the topology of the space of closed curves on $\Ss^2$which are locally convex (i.e., without inflection points).One of the main difficulties isthe absence of the covering homotopy principle for the map sending anon-closed locally convex curve to the Frenet frame at its endpoint.

Place, publisher, year, edition, pages
2012. Vol. 4, 1-22 p.
National Category
Geometry
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-70362DOI: 10.5427/jsing.2012.4aOAI: oai:DiVA.org:su-70362DiVA: diva2:480690
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Boris Shapiro
Available from: 2012-01-19 Created: 2012-01-19 Last updated: 2017-12-08Bibliographically approved

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