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The odd Vassiliev conjecture at four loops
- Speaker(s)
- Greg Kuperberg
- Affiliation
- University of California, Davis
- Language of the talk
- English
- Date
- Oct. 7, 2026, 10:30 a.m.
- Room
- room 4070
- Seminar
- Seminar Algebraic Topology
I will outline a proof that odd Jacobi diagrams vanish up to four loops, extending a result of Moskovich and Ohtuski by one. The implication for topology is that Vassiliev invariants up to degree four cannot distinguish an oriented knot from its inverse. My idea is to simplify calculations of Jacobi diagrams with a limited number of loops with the formalism of graph homology with polynomial coefficients, and using operadic composition of Jacobi diagrams with leaves. The calculation for three loops becomes much shorter, while the calculation for four loops becomes feasible without computer assistance.
