The deformation space of nonorientable hyperbolic 3–manifolds

Joan Porti Pique, Juan Luis Duran Batalla

Research output: Contribution to journalArticleResearchpeer-review


We consider nonorientable hyperbolic 3–manifolds of finite volume M3. When M3 has an ideal triangulation Δ, we compute the deformation space of the pair (M3,Δ) (its Neumann–Zagier parameter space). We also determine the variety of representations of π1(M3) in Isom(H3) in a neighborhood of the holonomy. As a consequence, when some ends are nonorientable, there are deformations from the variety of representations that cannot be realized as deformations of the pair (M3,Δ). We also discuss the metric completion of these structures and we illustrate the results on the Gieseking manifold.
Original languageEnglish
Pages (from-to)109-140
Number of pages32
JournalAlgebraic and Geometric Topology
Issue number1
Publication statusPublished - 18 Mar 2024


  • three-manifold, hyperbolic Dehn filling, nonorientable


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