2,459 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
Tilings of quadriculated annuli
Tilings of a quadriculated annulus A are counted according to volume (in the
formal variable q) and flux (in p). We consider algebraic properties of the
resulting generating function Phi_A(p,q). For q = -1, the non-zero roots in p
must be roots of unity and for q > 0, real negative.Comment: 33 pages, 12 figures; Minor changes were made to make some passages
cleare
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