Algebraization of Low-Dimensional Topology - Lecture 4

Explore the algebraic foundations of low-dimensional topology in this 57-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. Examine the concept of 3- and 4-modular Hopf algebras and their role in describing modified cobordism categories. Investigate the category of connected compact oriented 3-cobordisms between connected 1-punctured surfaces and the category of 4-dimensional 2-handlebodies. Learn how finite-dimensional and unimodular ribbon categories relate to 4-modular Hopf algebras and their potential for detecting 4-dimensional phenomena in non-semisimple and non-factorizable cases. Gain insights into cutting-edge research in algebraic topology and its applications to quantum field theories.