Composition Properties of Hyperbolic Links in Handlebodies

Triangulations of 3-manifolds, hyperbolic relative handlebodies, and Dehn filling

We establish a bijective correspondence between the set T(n) of 3-dimensional triangulations with n tetrahedra and a certain class H(n) of relative handlebodies (i.e. handlebodies with boundary loops, as defined by Johannson) of genus n+1. We show that the manifolds in H(n) are hyperbolic (with geodesic boundary, and cusps corresponding to the loops), have least possible volume, and simplest boundary loops. Mirroring the elements of H(n) in their geodesic boundary we obtain a class D(n) of cusped hyperbolic manifolds, previously considered by D. Thurston and the first named author. We show tha…

关于纽结柄体的对称性与外部问题

On symmetry and exterior problems of knotted handlebodies

研究3维球面中亏格2纽结柄体的对称性与外部问题，确定由非整数环面Dehn手术双曲纽结构造的柄体对称群并解决其外部问题，同时推广Lee-Lee族。

关于打结柄体的唯一分解

On unique decomposition of knotted handlebodies

本文研究了3-球中打结柄体沿分解2-球因式分解的唯一性问题，在特定条件下证明了唯一性，并据此确定了$6_{10}$的手性，构造了具有同胚外部的双曲柄体结无穷族。

The Chen-Yang volume conjecture for knots in handlebodies

In 2015, Chen and Yang proposed a volume conjecture that stated that certain Turaev-Viro invariants of an hyperbolic 3-manifold should grow exponentially with a rate equal to the hyperbolic volume. Since then, this conjecture has been proven or numerically tested for several hyperbolic 3-manifolds, either closed or with boundary, the boundary being either a family of tori or a family of higher genus surfaces. The current paper now provides new numerical checks of this volume conjecture for 3-manifolds with one toroidal boundary component and one geodesic boundary component. More precisely, we …

堆叠链的双曲性及体积下界

Hyperbolicity of Staked Links and Lower Bounds on Their Volumes

本文定义了堆叠链中的``魅力手链``，并提供了构造无限多个双曲链的方法，通过单个魅力的体积来确定其体积下界。

带边界加厚曲面上交错链环的双曲性

Hyperbolicity of Alternating Links in Thickened Surfaces with Boundary

本文研究了带边界加厚曲面上交错链环的双曲性，给出了判定补空间双曲性的简单条件，并推广至环境流形中的 tg-双曲性，为柄体、纤维丛及 staked 链环提供了大量双曲例子。