88 research outputs found
Homotopy type of spaces of curves with constrained curvature on flat surfaces
Let be a complete flat surface, such as the Euclidean plane. We determine
the homeomorphism class of the space of all curves on which start and end
at given points in given directions and whose curvatures are constrained to lie
in a given open interval, in terms of all parameters involved. Any connected
component of such a space is either contractible or homotopy equivalent to an
-sphere, and every is realizable. Explicit homotopy equivalences
between the components and the corresponding spheres are constructed.Comment: 39 pages, 13 figures. Differs from previous version by many
improvements of the expositio
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