Geodesic
Homology computations for complex braid groups
Journal of the European Mathematical Society, Tome 16 (2014) no. 1, pp. 103-164

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Complex braid groups are the natural generalizations of braid groups associated to arbitrary (finite) complex reflection groups. We investigate several methods for computing the homology of these groups. In particular, we get the Poincaré polynomial with coefficients in a finite field for one large series of such groups, and compute the second integral cohomology group for all of them. As a consequence we get non-isomorphism results for these groups.
DOI : 10.4171/jems/429
Classification : 20-XX, 00-XX
Keywords: Complex reflection groups, braid groups, group homology, Salvetti complex, Garside groups, Schur multiplier 
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Filippo Callegaro; Ivan Marin. Homology computations for complex braid groups. Journal of the European Mathematical Society, Tome 16 (2014) no. 1, pp. 103-164. doi: 10.4171/jems/429

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