Homework (2)

Recently, in September 2025, Roland van der Veen and myself released a paper titled "A Fast, Strong, Topologically Meaningful, and Fun Knot Invariant" (arXiv:2509.18456). More recently, in January 2025 in Les Diablerets (https://drorbn.net/ld26), I gave a talk in which I suggested 27 homework tasks related to that same invariant Θ (plus a bonus task). Today, after a brief review, I'll talk a bit more about just 4 of those tasks: • Figure out the relationship of Θ with Chern Simons theory. • Complete the discussion of the relationship of Θ with sl3. • Find formulas for Θ corresponding to other presentations of the Alexander module. • Fully understand Θ-like formulas and their non-uniqueness (i.e., clean the mess). More information and related materials are at: https://www.math.utoronto.ca/~drorbn/Talks/Banff-2607/