Mathematics – Geometric Topology
Scientific paper
2011-07-14
Mathematics
Geometric Topology
15 pages, 5 figures, 5 tables
Scientific paper
Agol has conjectured that minimally twisted n-chain links are the smallest volume hyperbolic manifolds with n cusps, for n at most 10. In his thesis, Venzke mentions that these cannot be smallest volume for n at least 11, but does not provide a proof. In this paper, we give a proof of Venzke's statement. The proof for n at least 60 is completely rigorous. The proof for n between 11 and 59 uses a computer calculation, and can be made rigorous for manifolds of small enough complexity, using methods of Moser and Milley. Finally, we prove that the n-chain link with 2m or 2m+1 half-twists cannot be the minimal volume hyperbolic manifold with n cusps, provided n is at least 60 or |m| is at least 8, and we give computational data indicating this remains true for smaller n and |m|.
Kaiser James
Purcell Jessica S.
Rollins Clint
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