The problem for the affine Artin group of type and its cohomology

  • Mario Salvetti

    Università di Pisa, Italy
  • Filippo Callegaro

    Scuola Normale Superiore, Pisa, Italy
  • Davide Moroni

    National Research Council of Italy (CNR), Pisa, Italy


We prove that the complement to the affine complex arrangement of type is a space. We also compute the cohomology of the affine Artin group (of type ) with coefficients in interesting local systems. In particular, we consider the module , where the first standard generators of act by -multiplication while the last generator acts by multiplication. Such a representation generalizes the analogous 1-parameter representation related to the bundle structure over the complement to the discriminant hypersurface, endowed with the monodromy action of the associated Milnor fibre. The cohomology of with trivial coefficients is derived from the previous one.

Cite this article

Mario Salvetti, Filippo Callegaro, Davide Moroni, The problem for the affine Artin group of type and its cohomology. J. Eur. Math. Soc. 12 (2010), no. 1, pp. 1–22

DOI 10.4171/JEMS/187