Combinatorialization of spaces of nondegenerate spherical curves

Victor Goulart, Nicolau Saldanha

A parametric curve $\gamma$ of class $C^n$ on the $n$-sphere is said to be nondegenerate (or locally convex) when $\det \left(\gamma (t),{\gamma }^{\prime }(t),\cdots ,{\gamma }^{(n)}(t)\right)>0$ for all values of the…