# Tagged Questions

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I am interested in the following situation: given a braid $B$, it induces a link $L$ in a pretty straightforward way ("glue" the endpoints, like here). For a braid $B$, we know how to represent it in ...
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### Properties of the Jones polynomial

Let $V(L)$ be the Jones polynomial of the oriented link $L$. For $\alpha \in B_n$, we write $V(\alpha)$ for $V(\hat{\alpha})$, where $\hat{\alpha}$ is the closed braid associated to $\alpha$. The ...
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### Markov Trace and Markov Property

Hey guys, I'm a computer science student attempting to understand a quantum algorithm that uses braid theory - something I'm completely unfamiliar. I've getting through the algorithm but I can't ...
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### Simplified Jones trace invariant for links

Jones (1985) defines a simplified trace invariant for knots by $W_K(t)=\frac{1-V_K(t)}{(1-t^3)(1-t)}$. Then, e.g., the Arf invariant for $K$ is $Arf(K)=W_K(i)$. Does this work for oriented links as ...
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Alexander's Theorem guarantees that every oriented link is the closure of some braid. In other words, the map $$\displaystyle \coprod\_n \mathcal B_n\longrightarrow \{\text{ oriented links }\}$$ ...
Artin's presentation of braid group on three strands is: $$B_3 = \langle l,r : lrl = rlr \rangle$$ where you should think of "$l$" as the positive crossing between the left and middle strands and ...