The hyperbolic complex line arrangement realization conjecture for quasipositive Seifert surfaces
The hyperbolic complex line arrangement realization conjecture for quasipositive Seifert surfaces
Let be a quasipositive Seifert surface. A proper arc in is an arc with endpoints on and interior in the interior of . Let be the surface used for plumbing, and let denote the surface obtained by plumbing copies of to along parallels of pairwise disjoint proper arcs . Hyperbolic complex line arrangement realization conjecture. There exists a system of pairwise disjoint proper arcs such that, for all sufficiently large , if is obtained by plumbing copies of along parallels of for , then is isotopic to the link at infinity of a hyperbolic -line arrangement. This would generalize the preceding theorem by realizing a broad class of links, obtained from quasipositive Seifert surfaces by sufficiently many such plumbings, as links at infinity of hyperbolic complex line arrangements; the source indicates that similar techniques may establish it, but does not provide a proof.
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Sources & referencesView supporting material
Primary source
Lee Rudolph, “Some fibered and non-fibered links at infinity of hyperbolic complex line arrangements”, arXiv:math/9912238 (2000).
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