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.References
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Additional Information
- Daniel C. Cohen
- Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
- MR Author ID: 290411
- ORCID: 0000-0002-5845-2523
- Email: cohen@math.lsu.edu
- Alexander I. Suciu
- Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
- MR Author ID: 168600
- ORCID: 0000-0002-5060-7754
- Email: alexsuciu@neu.edu
- 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. - © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 351 (1999), 4043-4067
- MSC (1991): Primary 14H30, 52B30, 57M05; Secondary 20F14, 20F36
- DOI: https://doi.org/10.1090/S0002-9947-99-02206-0
- MathSciNet review: 1475679