Geometry of planar surfaces and exceptional fillings. Issue 2 (17th January 2017)

• Record Type: Journal Article
• Authors: Hoffman, Neil R.; Purcell, Jessica S.
• Is Part Of: Bulletin of the London Mathematical Society. Volume 49:Issue 2(2017)
• Page Start: 185
• Page End: 201
• Publication Date: 2017-01-17
• Subjects: 57M50 (primary) -- 57M27 (secondary); Mathematics -- Periodicals; 510
• DOI: 10.1112/blms.12000
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract: If a hyperbolic 3‐manifold admits an exceptional Dehn filling, then the length of the slope of that Dehn filling is known to be at most six. However, the bound of six appears to be sharp only in the toroidal case. In this paper, we investigate slope lengths of other exceptional fillings. We construct hyperbolic 3‐manifolds that have the longest known slopes for reducible fillings. As an intermediate step, we show that the problem of finding the longest such slope is equivalent to a problem on the maximal density horoball packings of planar surfaces, which should be of independent interest. We also discuss lengths of slopes of other exceptional Dehn fillings, and prove that six is not realized by a slope corresponding to a small Seifert fibered space filling.