Some virtually special hyperbolic 3-manifold groups

Eric Chesebro, Jason DeBlois, Henry Wilton

Research output: Contribution to journalReview articlepeer-review

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 and deduce that such manifolds are virtually fibered. We generalise a theorem of Haglund andWise to the relatively hyperbolic setting and deduce that π 1M is LERF and that the geometrically finite subgroups of π 1M 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.

Original languageEnglish
Pages (from-to)727-787
Number of pages61
JournalCommentarii Mathematici Helvetici
Volume87
Issue number3
DOIs
StatePublished - 2012

Keywords

  • 3-manifold
  • Coxeter group
  • Virtual fibering
  • Virtual retract

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