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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.
Durán Batalla, Juan Luis 1 ; Porti, Joan 2
@article{10_2140_agt_2024_24_109,
author = {Dur\'an Batalla, Juan Luis and Porti, Joan},
title = {The deformation space of nonorientable hyperbolic 3{\textendash}manifolds},
journal = {Algebraic and Geometric Topology},
pages = {109--140},
publisher = {mathdoc},
volume = {24},
number = {1},
year = {2024},
doi = {10.2140/agt.2024.24.109},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.109/}
}
TY - JOUR AU - Durán Batalla, Juan Luis AU - Porti, Joan TI - The deformation space of nonorientable hyperbolic 3–manifolds JO - Algebraic and Geometric Topology PY - 2024 SP - 109 EP - 140 VL - 24 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.109/ DO - 10.2140/agt.2024.24.109 ID - 10_2140_agt_2024_24_109 ER -
%0 Journal Article %A Durán Batalla, Juan Luis %A Porti, Joan %T The deformation space of nonorientable hyperbolic 3–manifolds %J Algebraic and Geometric Topology %D 2024 %P 109-140 %V 24 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.109/ %R 10.2140/agt.2024.24.109 %F 10_2140_agt_2024_24_109
Durán Batalla, Juan Luis; Porti, Joan. The deformation space of nonorientable hyperbolic 3–manifolds. Algebraic and Geometric Topology, Tome 24 (2024) no. 1, pp. 109-140. doi: 10.2140/agt.2024.24.109
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