Quotient topology on the set of commensurability classes of hyperbolic 3-manifolds

摘要

We investigate relation between Dehn fillings and commensurability of hyperbolic 3-manifolds. The set consisting of the commensurability classes of hyperbolic 3-manifolds admits the quotient topology induced by the geometric topology. We show that this quotient space satisfies some separation axioms. Roughly speaking, this means that commensurability classes are sparsely distributed in the space consisting of the hyperbolic 3-manifolds. (C) 2020 Elsevier B.V. All rights reserved.