The deformation space of nonorientable hyperbolic 3–manifolds

Joan Porti Pique, Juan Luis Duran Batalla

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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.
Idioma originalEnglish
Pàgines (de-a)109-140
Nombre de pàgines32
RevistaAlgebraic and Geometric Topology
Estat de la publicacióPublicada - 18 de març 2024


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