On the total curvature of semialgebraic graphs
Abstract
Description
We define the total curvature of a semialgebraic embedding of a graph in the 3-dimensional Euclidean space. We prove that it satisfies a Chern-Lashof type inequality and we describe when the equality holds. We also prove a generalization of a classical result of Fary and Milnor stating that certain graphs cannot be knotted if they are not too curved. The techniques employed are Morse theoretic.
24 pages, 11 figures
24 pages, 11 figures