Geodesic
Image of the Burau representation at $d$-th roots of unity
T. N. Venkataramana1
1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai, 40005, India
Annals of mathematics, Tome 179 (2014) no. 3, pp. 1041-1083.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We show that the image of the braid group under the monodromy action on the homology of a cyclic covering of degree $d$ of the projective line is an arithmetic group provided the number of branch points is sufficiently large compared to the degree $d$. This is deduced by proving the arithmeticity of the image of the braid group on $n+1$ letters under the Burau representation evaluated at $d$-th roots of unity when $n\geq 2d$.
DOI : 10.4007/annals.2014.179.3.4

T. N. Venkataramana 1

1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai, 40005, India 
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T. N. Venkataramana. Image of the Burau representation at $d$-th roots of unity. Annals of mathematics, Tome 179 (2014) no. 3, pp. 1041-1083. doi : 10.4007/annals.2014.179.3.4. http://geodesic.mathdoc.fr/articles/10.4007/annals.2014.179.3.4/

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