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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Alexander invariants
of complex hyperplane arrangements


Authors: Daniel C. Cohen and Alexander I. Suciu
Journal: Trans. Amer. Math. Soc. 351 (1999), 4043-4067
MSC (1991): Primary 14H30, 52B30, 57M05; Secondary 20F14, 20F36
Published electronically: April 27, 1999
MathSciNet review: 1475679
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Daniel C. Cohen
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: cohen@math.lsu.edu

Alexander I. Suciu
Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
Email: alexsuciu@neu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02206-0
PII: S 0002-9947(99)02206-0
Keywords: Arrangement, braid monodromy, Alexander invariant, Chen groups
Received by editor(s): March 24, 1997
Received by editor(s) in revised form: September 9, 1997
Published electronically: April 27, 1999
Additional Notes: The first author was partially supported by grant LEQSF(1996-99)-RD-A-04 from the Louisiana Board of Regents and by a grant from the Louisiana State University Council on Research.
The second author was partially supported by N.S.F. grant DMS–9504833, and an RSDF grant from Northeastern University.
Article copyright: © Copyright 1999 American Mathematical Society