Given a braid (diagram) $\beta\in B_n$, the associated closed braid is the knot/link formed by attaching the ends on which the strings lie. We can also, however, think of $\beta$ as being an element of the mapping class group of the $n$-punctured disc $\text{Mod}(D_n)$. Is there a geometric interpretation of closed braids that comes from the mapping class group viewpoint?
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