Holonomic and Legendrian parametrizations of knots

Joan S. Birman, Nancy C. Wrinkle

Let $f:S^1\to R$ be a generic map. We may use $f$ to define a new map $\tilde{f}:S^1\to R^3$ by $\tilde{f}(t)=(-f(t),f^{\prime }(t),-f^{\prime \prime }(t))$, and if $f$ is an embedding then the image of…