论文标题
不可取向双曲线3型脉络的变形空间
The deformation space of non-orientable hyperbolic 3-manifolds
论文作者
论文摘要
我们认为不可定向的双曲线3个manifolds有限体积$ m^3 $。当$ m^3 $具有理想的三角剖分$δ$时，我们计算了一对$（m^3，δ）$（其Neumann Zagier参数空间）的变形空间。我们还确定了$π_1（m^3）$在$ \ mathrm {isom}（\ Mathbb {h}^3）$中的各种表示形式。结果，当某些末端是不可定向的时，从多种表示的变形，这些变形无法实现为对$（m^3，δ）$的变形。我们还讨论了这些结构的指标完成，并说明了吉赛克歧管上的结果。
We consider non-orientable hyperbolic 3-manifolds of finite volume $M^3$. When $M^3$ has an ideal triangulation $Δ$, we compute the deformation space of the pair $(M^3, Δ)$ (its Neumann Zagier parameter space). We also determine the variety of representations of $π_1(M^3)$ in $\mathrm{Isom}(\mathbb{H}^3)$ in a neighborhood of the holonomy. As a consequence, when some ends are non-orientable, there are deformations from the variety of representations that cannot be realized as deformations of the pair $(M^3, Δ)$. We also discuss the metric completion of these structures and we illustrate the results on the Gieseking manifold.
