Title | Alexander Invariants of Complex Hyperplane Arrangements |
Author(s) | Daniel C. Cohen, Alexander I. Suciu |
Type | Article in Journal |
Abstract | Let $A$ be an arrangement of $n$ complex hyperplanes. The fundamental group of the complement of $A$ is determined by a braid monodromy homomorphism, $a :F_{s}to P_{n}$. Using the Gassner
representation of the pure braid group, we find an explicit presentation for the Alexander invariant of $A$. From this presentation, we obtain combinatorial lower bounds for the ranks of
the Chen groups of $A$. We also provide a combinatorial criterion for when these lower bounds are attained. |
Keywords | Alexander invariants; Chen groups; Gassner representation; fundamental groups; braid monodromy homomorphisms; pure braid groups; presentations |
Length | 25 |
ISSN | 0002-9947 |
File |
|
URL |
http://www.ams.org/journal-getitem?pii=S0002-9947-99-02206-0 |
Language | English |
Journal | Transactions of the American Mathematical Society |
Volume | 351 |
Number | 10 |
Pages | 4043-4067 |
Publisher | American Mathematical Society |
Address | Providence, RI |
Year | 1999 |
Edition | 0 |
Translation |
No |
Refereed |
Yes |