Connections in low-dimensional topology

该项目旨在通过将双曲几何与量子拓扑、簇代数和旋量产生的不变量联系起来，解决低维拓扑中重要的悬而未决的问题。 在这个项目中研究的空间，即3-流形和结，出现在工程和科学的应用。该项目希望通过应用将它们与双曲几何连接起来的工具来产生对这些空间的新见解。 预期的成果包括有效的技术来计算重要的数据3-流形和结，特别是某些多项式编码的几何形状，并精确计算圆包装。 这应该会带来显著的好处，例如在双曲几何中的困难几何方面取得进展。

This project aims to resolve important open questions in low-dimensional topology, by connecting hyperbolic geometry to invariants arising from quantum topology, cluster algebras, and spinors. The spaces studied in this project, namely 3-manifolds and knots, arise in applications across engineering and science. The project expects to generate new insights into these spaces by applying tools connecting them to hyperbolic geometry. Expected outcomes include efficient techniques to compute important data about 3-manifolds and knots, particularly certain polynomials encoding geometry, and exact calculations of circle packings. This should provide significant benefits, such as progress on difficult conjectures in hyperbolic geometry.