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Alexander invariants of complex hyperplane arrangements |
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| Authors: | Daniel C. Cohen Alexander I. Suciu |
| Affiliation: | Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803 ; Department of Mathematics, Northeastern University, Boston, Massachusetts 02115 |
| Abstract: | Let  be an arrangement of  complex hyperplanes. The fundamental group of the complement of  is determined by a braid monodromy homomorphism,  . Using the Gassner representation of the pure braid group, we find an explicit presentation for the Alexander invariant of  . From this presentation, we obtain combinatorial lower bounds for the ranks of the Chen groups of  . We also provide a combinatorial criterion for when these lower bounds are attained. |
| Keywords: | Arrangement braid monodromy Alexander invariant Chen groups |
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