The University of Montana
Department of Mathematical Sciences

Technical report #2/2010

SOME VIRTUALLY SPECIAL HYPERBOLIC 3-MANIFOLD GROUPS

ERIC CHESEBRO, JASON DEBLOIS, AND HENRY WILTON

Abstract

Let M be a complete hyperbolic 3-manifold of finite volume that admits a decomposition into right-angled ideal polyhedra. We show that M has a deformation retraction that is a virtually special square complex, in the sense of Haglund and Wise. A variety of attractive properties follow: such manifolds are virtually fibered; their fundamental groups are LERF; and their geometrically finite subgroups are virtual retracts. Examples of 3-manifolds admitting such a decomposition include augmented link complements. We classify the low-complexity augmented links and describe an infinite family with complements not commensurable to any 3-dimensional reflection orbifold.

Keywords: hyperbolic 3-manifold, residual properties of groups, virtually fibered.

AMS Subject Classification: 20E26, 57M10

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