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In the late 90’s, Dennis Roseman described how to generalize Reidemeister moves on classical knots to higher dimensions. An isotopy can be generically projected just as a knot can. The generic self-intersection of an isotopy’s projection decomposes into a disjoint union of submanifolds. The cross-sections near the Morse theoretic critical points of these submanifolds give knot moves. I will talk about his proof, namely the 2-dimensional case, and how to bound the number of Reidemeister III moves needed to unknot a trivial link diagram by studying these isotopy projections.

Pizza at 11:50am.