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Knots and representation theory - Shared screen with speaker view
Мантуров Василий Олегович
37:21
Let's collect problems for future study.1) G_{n}^{k}, k>2, are generalisations of braids.What are generalisations of knots?Those should be curves in R^{k+1} where in each horizontal section R^{k} any k points are generic.2) There is a famous fibration: Stiefel over Grassman. How to generalize it to our spaces?3) Can our spaces serve as classifying spaces for some fibrations (maybe with sections or restrictions etc.)4) How to REALIZE the groups G_{n}^{k} as fundamental groups of configuration spaces.We have found these spaces for n=k+1;these are just configuration spaces on RP^{k-1}
Мантуров Василий Олегович
45:55
5) Study n-dimensional vector bundles bytransforming them into bundles of ^-products andinvent "braid characteristic elements" for such vector bundles.