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Knots and representation theory - Shared screen with speaker view
Мантуров Василий Олегович
Problem: Generalize skein-relations for 3-manifolds depending on homology/homotopy classes of "halves" (link component)
Мантуров Василий Олегович
Scientific problem.There is a way of constructing knot invariants (maybe to make it more fun, for knots in the full torus)by tracing the knot and writing some generators corresponding to crossings.Problem. Adopt it to the second Kirby move.The difficulty is as follows:We might expect that our knot invariant is valued in some LARGE GROUP. We may have two link components L_{1}, L_{2}and then swallow-followL_{1}#L_{2}, L_{2}.Now, the word for L_{1}#L_{2} will look terribly; it won't be just the product of two words: crossings of L_{2} will give rise to quadruple crossings and it is hard to trace what happens to the words.
Мантуров Василий Олегович
Next time (on June, 27) we'll have a talk by Mohammed Elhamdadi