Knots and links without parallel tangents

Details Knots and links without parallel tangents Knots and links without parallel tangents

1999-12-06

arxiv.org/abs/math/9912050v1

Mathematics

Geometric Topology

11 pages, 0 figures

Scientific paper

Steinhaus conjectured that every closed oriented $C^1$-curve has a pair of anti-parallel tangents. Porter disproved the conjecture by showing that there exist curves with no anti-parallel tangents. Colin Adams rised the question of whether there exists a nontrivial knot in $\R^3$ which has no parallel or antiparallel tangents. The main result of this paper solves this problem, showing that any (smooth or polygonal) link $L$ in $\R^3$ is isotopic to a smooth link $\hat L$ which has no parallel or antiparallel tangents.

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