Algebraization of Low-Dimensional Topology - Part II

Explore the algebraic foundations of low-dimensional topology in this 49-minute lecture by Anna Beliakova, part of the Workshop on Quantum symmetries at the Centre de recherches mathématiques. Delve into the classification of Topological Quantum Field Theories (TQFTs) in dimensions 2, 3, and 4, focusing on the algebraic presentation of cobordism categories. Learn about the concept of 3- and 4-modular Hopf algebras and their role in describing modified cobordism categories. Examine the structure of 4-dimensional 2-handlebodies and their organization into the category 4HB. Discover how finite-dimensional and unimodular ribbon categories relate to 4-modular Hopf algebras, and understand the potential of non-semisimple and non-factorizable unimodular ribbon categories in detecting 4-dimensional phenomena. This advanced mathematical lecture builds upon previous work by Bobtcheva and Piergallini, offering insights into the algebraization of low-dimensional topology.