Low-Dimensional Topology

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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.