2:00 pm Friday, October 9, 2020
Candidacy Talk: Composite Knots with Symmetric Union Diagrams by Feride Ceren Kose in Zoom
In the 1950s, Kinoshita and Terasaka introduced the notion of ‘union of knots’ which generalizes the operation of connected sum. An aesthetically appealing variation of this construction is a symmetric union, a union of a knot and its mirror. As the connected sum of a knot and its mirror is always ribbon, hence smoothly slice, symmetric unions too are ribbon. However, the converse is still an open question. Among candidates to be counterexamples, there are some composite ribbon knots. By studying their branched double covers I will give a short proof that they do not admit certain symmetric union presentations. Submitted by
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