The (p, q)-arithmetic hyperbolic lattices; p, q greater than or equal to 6

2015/02/19 by Colin Maclachlan, Maclachlan, Colin, Gaven Martin +1
Mathematics · #20H10 #22E40 #30D50 #30F40 #53A35 #57M60 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:20H10 #msc:22E40 #msc:30D50 #msc:30F40 #msc:53A35 #msc:57M60

paper · pdf · doi:10.48550/arxiv.1502.05453

arxiv created 2015/02/19 · arxiv updated 2015/02/20

Abstract

We prove there are exactly 16 arithmetic lattices of hyperbolic 3-space which are generated by two elements of finite orders p and q with p,q at least six. We also verify a conjecture of H.M. Hilden, M.T. Lozano, and J.M. Montesinos concerning the orders of the singular sets of arithmetic orbifold Dehn surgeries on two bridge knot and link complements.

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