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A small arithmetic hyperbolic three-manifold. (English) Zbl 0621.57006
It was shown by Jørgenson and Thurston that there is a minimal element $$v_ 1$$ in the set of volumes of complete orientable hyperbolic three- manifolds. Let M be the complete orientable hyperbolic 3-manifold resulting from (5,1) Dehn surgery on the complement of the figure-eight knot K in $$S^ 3$$. It is established in this paper that M is arithmetic. On the other hand, the author and Jørgenson have shown that there is an arithmetic manifold M’ with vol M’$$<vol M$$.
Reviewer: G.Soifer

##### MSC:
 57N10 Topology of general $$3$$-manifolds (MSC2010) 51M10 Hyperbolic and elliptic geometries (general) and generalizations 30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
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##### References:
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