Low-Dimensional Topology

低维拓扑是当前研究的一个非常活跃的领域，包括三维和四维的几何和拓扑的研究。随之而来的是结和表面的自然参与，以及丰富的代数结构集合和与物理研究的富有成效的互动。这个加拿大研究主席的目标是通过发展和解释看似无关的数学对象之间的相互作用，在低维拓扑学方面取得重要的新进展。这项工作的中心重点是揭示代数结构（特别是群上的序结构）、几何结构（特别是叶理）和低维现代同调不变量之间的深层联系。

Low-dimensional topology is a highly active area of current research that includes the study of geometry and topology in dimensions three and four. With this comes a natural involvement of knots and surfaces, as well as a rich collection of algebraic structures and a fruitful interaction with research from physics. The objective of this Canada Research Chair is to make important new progress in low-dimensional topology by developing and explaining the interaction between seemingly unrelated mathematical objects. The central focus of this work is to uncover deep connections between algebraic structures (particularly, order structures on groups), geometric structures (particularly, foliations), and modern homological invariants in low-dimensions.