The ribbon-knot symmetric-union conjecture

A ribbon knot is a knot admitting a ribbon-disk presentation, and a symmetric union is a knot diagram obtained by joining two knots symmetrically across an axis, with the resulting diagram invariant under reflection in that axis.

Ribbon-knot symmetric-union conjecture. Every ribbon knot is a symmetric union.

The conjecture asserts that all ribbon knots admit symmetric-union presentations. The source lists proving it as a project and gives no general proof, so it remains open there.

Sources & referencesView supporting material

Primary source

Christoph Lamm, “Symmetric union presentations for 2-bridge ribbon knots”, arXiv:math/0602395 (2022).

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