On Thurston's "geometric ideal triangulation" conjecture

发布时间：2023-09-18 作者：浏览次数：

Speaker:	葛化彬	DateTime:	2023年9月21日（周四）上午8:30-9:30
Brief Introduction to Speaker: 葛化彬，华中科技大学数学与应用数学系本科，北京大学数学科学学院博士，北京国际数学研究中心博士后，现为中国人民大学数学学院教授，博士生导师。主要研究方向为几何拓扑，推广了柯西刚性定理和Thurston圆堆积理论，部分解决Thurston的“几何理想剖分”猜想、完全解决Cheeger-Tian、林芳华的正则性猜想，相关论文分别发表在Geom. Topol., Geom. Funct. Anal., Amer. J. Math., Adv. Math.等著名数学期刊。		Place:	6号楼2楼报告厅
Abstract:Gluing ideal tetrahedra plays a crucial role in the construction of hyperbolic 3-manifolds. On the contrary, it is still not known that whether a hyperbolic 3-manifold admits a geometric ideal triangulation. One of the greatest achievment in three dimensional topology is the famous Hyperbolic Dehn filling Theorem. It was proved by Thurston at the end of the 1970s under the assumption that all cusped hyperbolic 3-manifolds admits a geometric triangulation. In this talk, We will show our program to hyperbolize and further obtain geometric triangulations of 3-manifolds. To be precise, we will show the connections between 3D-combinatorial Ricci flows and Thurston's geometric triangulations, that is, for a particular triangulation, the flow converges if and only if the triangulation is geometric. We will also give some topological conditions to guarantee the convergence of the combinatorial Ricci flows and furthermore the existence of geometric ideal triangulations. As far as we know, th...

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