Some fibered and non-fibered links at infinity of hyperbolic complex line arrangements
| dc.creator | Rudolph, Lee | |
| dc.date | 1999-12-31 | |
| dc.date | 2000-07-09 | |
| dc.date.accessioned | 2026-07-07T05:32:34Z | |
| dc.date.available | 2026-07-07T05:32:34Z | |
| dc.description | Let F be R or C, d the dimension of F over R. Denote by P(F) either the affine plane A(F) or the hyperbolic plane H(F) over F. An arrangement L of k lines in P(F) (pairwise non-parallel in the hyperbolic case) has a link at infinity K(L) comprising k unknotted (d-1)-spheres in the (2d-1)-sphere, whose topology reflects the combinatorics of L `at infinity'. The class of links at infinity of affine F-line arrangements is properly included in the class of links at infinity of hyperbolic F-line arrangements. Many links at infinity of (essentially non-affine) connected hyperbolic C-line arrangements are far from being fibered; the proof is a direct construction, using ``Legendrian inscription''. In contrast, if the (affine or hyperbolic) R-line arrangement L is connected, then its complexification (an affine or hyperbolic C-line arrangement) has a fibered link at infinity; the proof uses A'Campo's divides. | |
| dc.description | Revised and expanded (figures added); 12 pages, 5 figures; accepted for publication in the Special Issue of the journal Topology and its Applications devoted to the "Arrangements in Boston" Conference (1999) | |
| dc.identifier | https://arxiv.org/abs/math/9912238 | |
| dc.identifier | http://arxiv.org/abs/math/9912238 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79702 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M25, 52B30, 51M99 (Primary) | |
| dc.title | Some fibered and non-fibered links at infinity of hyperbolic complex line arrangements | |
| dc.type | text |