Timeline for Different flavours of Vassiliev Conjecture
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 28, 2023 at 23:13 | vote | accept | Andrea Marino | ||
| Aug 18, 2023 at 10:01 | comment | added | Geoffroy Horel | Regarding the first proof of rational [TVC] I think indeed, the first written record is our paper. Weirdly enough Arone Lambrechts Turchin and Volic did not prove rational collapse of the homotopy spectral sequence for long knots in $\mathbb{R}^3$. | |
| Aug 17, 2023 at 20:30 | comment | added | Geoffroy Horel | Andrea, this statement of Kontsevich is about the homological Vassiliev spectral sequence, so everything is fine if you replace $\pi_0$ by $H_0$ in your statement of CVC | |
| Aug 17, 2023 at 15:15 | comment | added | Andrea Marino | Another question: I am citing your work with De Brito as the first proof of rational [TVC]. You proved that $\pi_0(T_{n+1}\mathcal{K}) \otimes \mathbb{Q} $ can be described in terms of chord diagrams, and the same expression holds for $(\pi_0(\mathcal{K})/\sim_n ) \otimes \mathbb{Q}$ by Konsevithc Realization Theorem. Is there an earlier appearance of this result, as far as you know? Thanks. | |
| Aug 17, 2023 at 15:13 | comment | added | Andrea Marino | Geoffroy, thank you very much for your commitment to careful explanations: you will definitely land on my PhD acknowledgment section :D I thought that [CCH] implied [CVC] because of Konsevitch's remark in his famous article "Vassiliev's Knot Invariants", after theorem 2.1: "This theorem [that is, $ V_k / V_{k-1} \simeq A_k^*$ over real numbers] means that differentials for zero cohomology groups of the space of knots in higher terms of Vassiliev's spectral sequence are trivial up to torsion". What's wrong with the intuition I outlined? Aren't second and $\infty$ pages described as I did? | |
| Aug 14, 2023 at 6:55 | history | answered | Geoffroy Horel | CC BY-SA 4.0 |