7 papers
A CW complex homotopy equivalent to spaces of locally convex curves
Victor Goulart, Nicolau C. Saldanha
Locally convex curves in the sphere have been studied for several reasons, including the study of linear ordinary differential equations. Taking Frenet frames obtains corresp…
Homotopy type of spaces of locally convex curves in the sphere S^3
EmÃlia Alves, Victor Goulart, Nicolau C. Saldanha
Locally convex (or nondegenerate) curves in the sphere have been studied for several reasons, including the study of linear ordinary differential equations of order . Ta…
Homotopy type of spaces of curves with constrained curvature on flat surfaces
Nicolau C. Saldanha, Pedro Zühlke
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…
Domino tilings beyond 2D
Caroline J. Klivans, Nicolau C. Saldanha
There is a rich history of domino tilings in two dimensions. Through a variety of techniques we can answer questions such as: how many tilings are there of a given region or what d…
Stability of compact actions and a result on divided differences
Carlos Gustavo Moreira, Nicolau C. Saldanha
We study smooth locally free actions of on manifolds of dimension . We are interested in compact orbits and in compact actions: actions with all orbits com…
Relative Helicity and Tiling Twist
Boris Khesin, Nicolau C. Saldanha
We consider domino tilings of 3D cubiculated regions. The tilings have two invariants, flux and twist, often integer-valued, which are given in purely combinatorial terms. These in…