All Questions
Tagged with quandles self-distributivity
7 questions
2
votes
0
answers
108
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Is the action of free self-distributive algebras on racks computable in polynomial time?
Let $B_{\infty}$ denote the infinite strand braid group. Let
$\mathrm{sh}:B_{\infty}\rightarrow B_{\infty}$ be the mapping where
$\mathrm{sh}(\sigma_{i})=\sigma_{i+1}$ whenever $i\geq 1$. Then
$B_{\...
12
votes
0
answers
259
views
Higher homotopical information in racks and quandles
A quandle is defined to be a set $Q$ with two binary operations $\star,\bar\star\colon\ Q\times Q\to Q$ for which the following axioms hold.
Q1. a $\star$ a = a
Q2. (a $\star$ b) $\bar\star$ b = (a $\...
4
votes
1
answer
244
views
Quandle homomorphism does not always induces group homomorphism on inner automorphism groups of quandles
Let $X$ and $Y$ be two quandles and $f: X \rightarrow Y$ be a quandle homomorphism. Then we can define a map $\bar f: Inn(X) \rightarrow Inn(Y)$ as $\bar f(S_a)=S_{f(a)}$, where $a \in X$. Then $\bar ...
- 163
7
votes
0
answers
342
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Hemi-semi direct product of racks or quandles
In the category of racks (similarly quandles), instead of well-known semidirect product, we have the hemi-semi direct product construction as seen on Wagemann & Crans.
As far as I know, semi ...
- 191
10
votes
4
answers
2k
views
Conjugation Quandles and... "Quandle-Groups"? From quandles to Groups
This question is already asked MathSE
A quandle $(Q,*,/ )$ is a idempotent right-distributive and right invertible structure.
1) $a*a=a$
2) $(a*b)*c=(a*c)*(b*c)$
3) $(a*b) /b=(a/b)*b=a$
...
- 233
5
votes
1
answer
403
views
One question about the quandle
Given a finite quandle $Q$, for any knot $K$ one can associate an invariant, i.e. the number of proper colorings $p(K)$. Let us consider the inverse $K^{-1}$ and mirror image $K'$ of $K$. My queston ...
- 517
16
votes
2
answers
602
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Formally undecidable problems on finitely presented quandles
In the literature, one sometimes sees the claim that finitely presented quandles (in particular, knot quandles) are "hard to deal with". Hence, a great deal of effort has gone into studying finite ...
- 1,889