Homology of braid groups, the Burau representation, and points on superelliptic curves over finite fields

Weiyan Chen

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)739-762
Number of pages24
JournalIsrael Journal of Mathematics
Volume220
Issue number2
DOIs
StatePublished - Jun 1 2017

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