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Knots and links without parallel tangents | | Ying-Qing Wu
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6 Dec 1999 | | Subject: | Geometric Topology MSC-class: 57M25 | math.GT | | Abstract: | 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. | | Source: | arXiv, math.GT/9912050 | | Services: | Forum | Review | PDF | Favorites | |
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