Projects per year
Abstract
If a hyperbolic 3manifold 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 3manifolds 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.
Original language  English 

Pages (fromto)  185201 
Number of pages  17 
Journal  Bulletin of the London Mathematical Society 
Volume  49 
Issue number  2 
DOIs  
Publication status  Published  1 Apr 2017 
Keywords
 57M27 (secondary)
 57M50 (primary)
Projects
 1 Finished

Quantum invariants and hyperbolic manifolds in threedimensional topology
Australian Research Council (ARC), Monash University
1/01/16 → 31/07/20
Project: Research