Artin kernels and Milnor fibrations of arrangements

It has long been recognized that there are many fruitful connections between the protagonists of this workshop: hyperplane arrangements and Artin groups. I will discuss in this talk a connection between two kinds of fibrations that occur in these contexts. One is the Milnor fibration of the complement of an arrangement of complex hyperplanes (perhaps taken with multiplicities) over the circle. The other is an "algebraic fibration" of the right-angled Artin group associated to a graph (perhaps with weights assigned to the vertices) over the integers. In either case, one is interested in the topological invariants of the fiber (or the kernel), be it the Milnor fiber of the (multi-)arrangement, the Bestvina-Brady group of the graph, or the Artin kernel of the weighted graph. After a brief overview of these topics, I will focus on the case when the monodromy of the aforementioned fibrations is trivial in homology, and I will outline several new results in this direction, some of which can be stated in a unified way.

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