Abstract:
We construct an interesting invariant for braids, the secant-quandle (SQ), derived from homotopy classes of generic secants and generic trisecants. We provide an algebraic-topological interpretation of this invariant by showing that each generator in SQ corresponds to a special element of the fundamental group of the braid complement, specifically, a meridian encircling exactly two braid strands. This interpretation enables a natural generalization of the secant-quandle to an invariant of knots and links, the loop-quandle (LQ). Furthermore, we extend the construction to the virtual braids. As an application, we compute the SQ and LQ for the Hopf link.
Language: English
Website:
https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1hVV0tvN0xWdXRsV2pnQT09
|
