Algebraic Presentations of 4- and 3-Manifolds in Low-Dimensional Topology

Explore algebraic presentations of 4- and 3-manifolds in this 53-minute lecture by Anna Beliakova at the Centre de recherches mathématiques (CRM). Delve into the categories of n-cobordisms, a fundamental concept in low-dimensional topology. Examine the classification of 2Cob as a monoidal category generated by its commutative Frobenius algebra object, and learn how this result impacts TQFT functors. Discover similar findings for n=3 and n=4, developed in collaboration with Ivelina Bobtcheva, Marco De Renzi, and Riccardo Piergallini. Understand the role of braided Hopf algebras as an analogue to Frobenius algebras in higher dimensions. Connect these concepts to the Andrews-Curtis conjecture, a notable problem in combinatorial group theory. This talk is part of the Workshop on Quantum Symmetries, focusing on tensor categories, topological quantum field theories, and vertex algebras.