Tagged Questions
3
votes
0answers
27 views
Alexanderpolynomial of connected sum via Fox calculus and Wirtinger presentation
Hello :) i have just reading the question "How to compute the Alexander polynomial of general torus knot" and i was suprised how strong it works if someone have a difficult question. I am also very ...
2
votes
0answers
29 views
Alexanderpolynomial of torus knot
i want to compute the Alexanderpolynomial of the torus knot $T_{p,q}$ with $p$ and $q$ coprime. I should work with the groups presentation $G(T_{p,q})=<x,y:x^p=y^q>$ of $T_{p,q}$. I have to use ...
2
votes
1answer
119 views
Dehn presentation proof reference request
Can someone give me a reference for a proof that the Dehn presentation of a knot group gives us the fundamental group of the knot complement in $S^{3}$?
0
votes
1answer
76 views
Pure braid group, stabilizer
From group theory we know that a homomorphism $\phi: G \to \operatorname{Sym}(S)$, where S is a set, then $\operatorname{Sym}(S) \cong \Sigma_n $. Its kernel is given as $\bigcap_{s \in S}G_s$, which ...
9
votes
1answer
239 views
Can the n-string sphere braid group embed in to the (n+1)-string sphere braid group?
This question has been cross posted on MathOverflow with some very interesting answers and discussion.
I'm currently writing a project on the braid groups and their analogues on closed surfaces. ...
2
votes
0answers
111 views
Computing knot/link groups
The knot group of a knot $K$ is the fundamental group of $\mathbb R^3 \smallsetminus K$; that is, the set of possibly self-crossing closed paths (starting and ending at any single point in space) ...
