JournalscmhVol. 87, No. 3pp. 727–787

Some virtually special hyperbolic 3-manifold groups

  • Eric Chesebro

    University of Montana, Missoula, USA
  • Jason DeBlois

    University of Pittsburgh, USA
  • Henry Wilton

    University of Cambridge, Great Britain
Some virtually special hyperbolic 3-manifold groups cover
Download PDF

Abstract

Let MM be a complete hyperbolic 3-manifold of finite volume that admits a decomposition into right-angled ideal polyhedra. We show that MM has a deformation retraction that is a virtually special square complex, in the sense of Haglund and Wise and deduce that such manifolds are virtually fibered. We generalise a theorem of Haglund and Wise to the relatively hyperbolic setting and deduce that π1M{\pi_1}M is LERF and that the geometrically finite subgroups of π1M{\pi_1}M 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.

Cite this article

Eric Chesebro, Jason DeBlois, Henry Wilton, Some virtually special hyperbolic 3-manifold groups. Comment. Math. Helv. 87 (2012), no. 3, pp. 727–787

DOI 10.4171/CMH/267