| 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 |
