On the total curvature of semialgebraic graphs

Details On the total curvature of semialgebraic graphs On the total curvature of semialgebraic graphs

2008-06-23

arxiv.org/abs/0806.3683v1

Mathematics

Geometric Topology

24 pages, 11 figures

Scientific paper

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.

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