Transactions of the American Mathematical Society

Author(s): Daniel C. Cohen; Alexander I. Suciu
Journal: Trans. Amer. Math. Soc. 351 (1999), 4043-4067.
MSC (1991): Primary 14H30, 52B30, 57M05; Secondary 20F14, 20F36
Posted: April 27, 1999
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Abstract: Let $\mathcal{A}$ be an arrangement of

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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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 14H30, 52B30, 57M05, 20F14, 20F36

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: 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
Posted: 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.
Copyright of article: Copyright 1999, American Mathematical Society

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