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Contributed talk - Extended evaluation maps from knots to the embedding tower

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HHHW04 - Manifolds

The evaluation maps from the space of knots to the associated embedding tower are conjectured to be universal knot invariants of finite type. Currently such invariants are known to exist only over the rationals (using the existence of Drinfeld associators) and the question of torsion remains wide open. On the other hand, grope cobordisms are certain operations in ambient 3-space producing knots that share the same finite type invariants and give a geometric explanation for the appearance of Lie algebras and graph complexes.

I will explain how grope cobordisms and an explicit geometric construction give paths in the various levels of the embedding tower. Taking components recovers the result of Budney-Conant-Koytcheff-Sinha, showing that these invariants are indeed of finite type. This is work in progress joint with Y. Shi and P. Teichner.

This talk is part of the Isaac Newton Institute Seminar Series series.

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