Homology of braid groups, the Burau representation, and points on superelliptic curves over finite fields
نویسنده
چکیده
The (reduced) Burau representation Vn of the braid group Bn is obtained from the action of Bn on the homology of an infinite cyclic cover of the disc with n punctures. In this paper, we calculate H∗(Bn;Vn). Our topological calculation has the following arithmetic interpretation (which also has different algebraic proofs): the expected number of points on a random superelliptic curve of a fixed genus over Fq is q.
منابع مشابه
Homology of braid groups, the Burau representation, and Fq-points on superelliptic curves
The (reduced) Burau representation Vn of the braid group Bn is obtained from the action of Bn on the homology of an infinite cyclic cover of the disc with n punctures. In this paper, we calculate H∗(Bn;Vn). As an application, we show that the expected number of Fq-points on a random superelliptic curve is equal to q.
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تاریخ انتشار 2017