Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am reading p.56 in the book (p.69 in the pdf file), and trying to understand the proof that quandles completely determine knots up to orientation.

The only thing I understand is that it tries to show that $ana^{-1} = an^{-1}a^{-1}$ which would mean $n = n^{-1}$ and since $n$ is an element in the fundamental group of a torus, isomorphic to $\mathbb{Z}^2$, this means that $2n = (0,0)$, i.e. $n =(0, 0)$. After some rereading, I find that the book seems to point to the fact that the normalizer of the meridian is isomorphic to the fundamental group of the torus $\partial N(K)$. But why is it so?

An explanation that aids understanding of the proof would be very much appreciated.

share|cite|improve this question
up vote 2 down vote accepted

See page 52 of Joyce's 1979 dissertation An Algebraic Approach to Symmetry with Applications to Knot Theory

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.