A program to construct integer-valued finite-type knot invariants
6.04.2017
| Date | 6.04.2017 |
|---|---|
| Time | 15:15 |
| Place |
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| Speaker | Dev Sinha |
| Area of expertise | Physics |
| Host | Dep. Physik |
| Contact | |
| Abstract | Using techniques closely related to his celebrated work in deformation theory, Kontsevich constructed an explicit, geometric universal Vassiliev invariant over the real numbers (or by deep results, over the rational numbers). Vassiliev invariants over the integers are far from settled. We outline a program to investigate them using the Goodwillie-Weiss tower for the embedding functor. We recently showed this tower has needed structure and provided spectral sequence evidence for the conjecture that the tower serves as a universal finite-type invariant over the integers. We have also developed Hopf invariants for homotopy groups and now more general mapping sets, which have the potential to detect components of the tower. We describe these two lines of progress and then ideas for next steps. |