Pacific Journal of Mathematics · 1993 · 134 citations · 12 references
Natural SciencesMathematicsCombinatoricsGeometryTopologyAlgebraic GeometryFundamental GroupGeometric TopologyGroup TheoryKnot TheoryBraid DiagramsBraid GroupsBraid TheoryLink TheoryNormal Form Representation
A complete solution is given to the classification problem for oriented links which are closed three-braids. The Classification Theorem asserts that, up to a finite list of exceptional cases, links which can be represented by closed 3-braids are represented by a unique conjugacy class in the group of 3-braids. The exceptional cases are the expected ones (links of braid index 1 and 2) and an unexpected infinite family of invertible links, each member of which has two 3braid axes. The two axes correspond to diagrams which are related by "braid-preserving flypes".
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A Lemma on Systems of Knotted Curves
James Alexander · Proceedings of the National Academy of Sciences · 1923 · 500 citations · Full text
On the Jones polynomial of closed 3-braids
Joan S. Birman · Inventiones mathematicae · 1985 · 75 citations