Some fibered and non-fibered links at infinity of hyperbolic complex line arrangements

dc.creatorRudolph, Lee
dc.date1999-12-31
dc.date2000-07-09
dc.date.accessioned2026-07-07T05:32:34Z
dc.date.available2026-07-07T05:32:34Z
dc.descriptionLet 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.descriptionRevised 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.identifierhttps://arxiv.org/abs/math/9912238
dc.identifierhttp://arxiv.org/abs/math/9912238
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79702
dc.subjectGeometric Topology
dc.subject57M25, 52B30, 51M99 (Primary)
dc.titleSome fibered and non-fibered links at infinity of hyperbolic complex line arrangements
dc.typetext

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