Distinct transverse knots remain distinct as virtual transverse knots
Distinct transverse knots remain distinct as virtual transverse knots
An ordinary transverse knot is an equivalence class of ordinary braids modulo conjugation and positive stabilization. A virtual transverse knot is an equivalence class of one-component virtual braid closures modulo conjugation and positive stabilization. Every transverse knot therefore determines a virtual transverse knot.
Transverse-to-virtual injectivity conjecture. No two transverse knots are the same virtual transverse knot.
The conjecture asks whether passing from ordinary transverse knots to virtual transverse knots loses no information. Its resolution is not supplied in the source.
Sources & referencesView supporting material
Primary source
Cole Hugelmeyer, “Diagram Systems and Generalized Finite Type Theories”, arXiv:2307.07661 (2023).
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