TY - JOUR
T1 - Homology of braid groups, the Burau representation, and points on superelliptic curves over finite fields
AU - Chen, Weiyan
N1 - Publisher Copyright:
© 2017, Hebrew University of Jerusalem.
PY - 2017/6/1
Y1 - 2017/6/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s11856-017-1534-7
DO - 10.1007/s11856-017-1534-7
M3 - Article
AN - SCOPUS:85019574683
SN - 0021-2172
VL - 220
SP - 739
EP - 762
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 2
ER -