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On Milnor fibrations of arrangements. (English) Zbl 0814.32007
We use covering space theory and homology with local coefficients to study the Milnor fiber of a homogeneous polynomial. These techniques are applied in the context of hyperplane arrangements, yielding an explicit algorithm for computing the Betti numbers of the Milnor fiber of an arbitrary real central arrangement in \(\mathbb{C}^ 3\), as well as the dimensions of the eigenspaces of the algebraic monodromy. We also obtain combinatorial formulas for these invariants of the Milnor fiber of a generic arrangement of arbitrary dimension using these methods.

MSC:
32S55 Milnor fibration; relations with knot theory
32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
55N25 Homology with local coefficients, equivariant cohomology
57M05 Fundamental group, presentations, free differential calculus
20F36 Braid groups; Artin groups
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