Alexander invariants of complex hyperplane arrangements

Cohen, Daniel; Suciu, Alexander

doi:10.1090/S0002-9947-99-02206-0

Alexander invariants of complex hyperplane arrangements
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by Daniel C. Cohen and Alexander I. Suciu PDF

Trans. Amer. Math. Soc. 351 (1999), 4043-4067 Request permission

Abstract:

Let $\mathcal {A}$ be an arrangement of $n$ complex hyperplanes. The fundamental group of the complement of $\mathcal {A}$ is determined by a braid monodromy homomorphism, $\alpha :F_{s}\to P_{n}$. Using the Gassner representation of the pure braid group, we find an explicit presentation for the Alexander invariant of $\mathcal {A}$. From this presentation, we obtain combinatorial lower bounds for the ranks of the Chen groups of $\mathcal {A}$. We also provide a combinatorial criterion for when these lower bounds are attained.

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