It sounds like a wiggle of the standard degeneracy locus interpretation in G/H and my lecture notes (proved with Schubert cycles in the universal case).
I was sick for a few days post-vaccination and kept thinking about random things. Someone asked me about quandle homology and I went into a quandle rabbithole.
My exercise is: Construct a sequence of continuous functions $f_n : [0, 1] → [−1, 1]$ such that $\int_0^1 f_n(x) dx = 0$ for all $n$ and $f_n(x)$ does not converge for any $x\in [0, 1]$. Now I'm asking myself if $f_n(x)=\sin(\pi \cdot n)$ is a valid solution? (sorry to interrupt here)
A natural example of a rack is a group with binary operation being $a * b = aba^{-1}$. Then $a * (b * c) = a(bcb^{-1})a^{-1} = aba^{-1} aca^{-1} ab^{-1} a^{-1} ac^{-1}a^{-1} = (a * b) * (a * c)$.
Ah, alas. Well, long story short, given any link you can do the following: Whenever there's a crossing you can draw 3 loops, one which winds around the overcrossing, one which winds around one half of the undercrossing, and one which winds around the other half of the undercrossing
@TedShifrin: I found my post. What I had proven was that the Binomial Transform of $-H_n$ is $\frac1n[n>0]$, but since the Binomial Transform is its own inverse, I had what I wanted (that the Binomial Transform of $-\frac1n[n>0]$ is $H_n$).
The link group is a really dumb invariant of the link. For a knot, the knot group is typically good but because of chance: There is a famous theorem of Gordon-Luecke which says knots are isotopic iff the knot complements are homeomorphic. There is also a famous theorem of Papakyriakapoulos which says knot complements are $K(G, 1)$, so determined by their fundamental groups, upto homotopy.
And there is also a famous theorem of Thurston which says knot complements are mostly hyperbolic, and finally hyperbolization theorem says hyperbolic manifolds are often determined by fundamental group and some extra structure at the end...
However, the above chain of reasoning has a screeching hault at the very beginning for links. Gordon-Luecke theorem fails. It's really easy to come up with non-isotopic links with homeomorphic complements.
So the link group is going to lose a lot of info
Some genius had the following idea: Instead of creating this link group with $a, b, c$, $aba^{-1} = c$, why not create a rack generated by $a, b, c$, $a*b = c$?
Almost by construct, you lose no information. Unfortunately, racks are insane new notions and studying them would mean you have to create foundations for racks like people for the past few centuries have been creating foundations for groups
So that's the story
I'm actually being tongue and cheek. It's an insane idea but you can extract very good link invariants from the fundamental rack. This is by Rourke and Sanderson.
