The reduced Burau representation $V_n$ of the braid group $B_n$ is obtained from the action of $B_n$ on the homology of an infinite cyclic cover of the $n$-punctured disc. In this note, we calculate $H_*(B_n;V_n)$ as a module over the Laurent polynomial ring $\mathbb{Q}[t,t^{-1}]$.
The kernel of $Burau(4) \otimes Z_p$ is all pseudo-Anosov
Homology of braid groups, the Burau representation, and $\mathbb{F}_q$-points on superelliptic curves
Categorified invariants and the braid group
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