Low Dimensional Topology

July 14, 2008

A theta curve containing three trefoils

Filed under: 3-manifolds,Knot theory — Jesse Johnson @ 9:39 am

Back in May I pointed out a paper on spacial graphs [1] that answered a question I had asked earlier: whether it is possible to embed a theta graph in the 3-sphere so that each of the three knots that result from removing edges is a trefoil. (They actually prove a more general property for a larger family of graphs.)  Akira Yasuhara, one of the authors of the paper has just sent me a link to a picture of a theta graph containing three trefoils.   It’s surprisingly simple.  Thanks Akira.

[1] Realization of knots and links in a spatial graph. (English summary) Topology Appl. 112 (2001), no. 1, 87–109.

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