Trisections, triangulations and the complexity of manifolds

该项目旨在根据应用程序的需要实际表示3维和4维空间。拓扑学是对空间形状的数学研究。几何赋予空间额外的结构，如距离，角度和曲率。特殊的组合结构，如极小三角剖分，往往与几何结构或拓扑性质密切相关。该项目旨在构建可计算的不变量，三角剖分的连通性结果，以及识别基本拓扑性质和结构（如三分和束）的算法。

This project aims at practical representations of 3-dimensional and 4-dimensional spaces as needed in applications. Topology is the mathematical study of the shapes of spaces. Geometry endows spaces with additional structure such as distance, angle and curvature. Special combinatorial structures, such as minimal triangulations, are often closely connected to geometric structures or topological properties. This project aims to construct computable invariants, connectivity results for triangulations, and algorithms to recognise fundamental topological properties and structures such as trisections and bundles.