On the monodromy action on Milnor fibers of graphic arrangements

Abstract

We analyze the monodromy action, over the rationals, on the first homology group of the Milnor fiber, for arbitrary subarrangements of Coxeter arrangements. We propose a combinatorial formula for the monodromy action, involving Aomoto complexes in positive characteristic. We verify the formula, in cases A, B and D.

arXiv comment23 pages; updated references

References in corpus (3)

• Fundamental groups of line arrangements: Enumerative aspects
• The spectral sequence of an equivariant chain complex and homology with local coefficients
• Cohomology of the Orlik-Solomon algebras and local systems

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• Homology graph of real arrangements and monodromy of Milnor Fiber
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• On the monodromy of Milnor fibers of hyperplane arrangements
• Milnor fibrations of arrangements with trivial algebraic monodromy
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• Non-crossing partitions and Milnor fibers
• On the topology of the Milnor fibration of a hyperplane arrangement
• Some computations on the characteristic variety of a line arrangement
• A survey of combinatorial aspects in the topology of complex hyperplane arrangements
• Lowest non-zero vanishing cohomology of holomorphic functions