Hyperplane arrangements and Milnor fibrations

Suciu, Alexander I.

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Numéro Spécial à l’occasion de la conférence Arrangements in Pyrénées, Pau 11-15 juin 2012, Tome 23 (2014) no. 2, pp. 417-481.

Étant donné un arrangement d’hyperplans, il y a plusieurs espaces topologiques qu’on peut lui associer : le complémentaire et sa variété bord, ainsi que la fibre de Milnor et son bord. Tous ces espaces sont reliés, en premier lieu par des fibrations. On utilise la cohomologie avec coefficients dans les systèmes locaux de rang $1$ sur le complémentaire d’un arrangement d’hyperplans pour étudier l’homologie des trois autres espaces, et les opérateurs de monodromie des fibrations associées.

There are several topological spaces associated to a complex hyperplane arrangement: the complement and its boundary manifold, as well as the Milnor fiber and its own boundary. All these spaces are related in various ways, primarily by a set of interlocking fibrations. We use cohomology with coefficients in rank $1$ local systems on the complement of the arrangement to gain information on the homology of the other three spaces, and on the monodromy operators of the various fibrations.

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