Algebraic Presentations of 4- and 3-Manifolds in Low-Dimensional Topology
Offered By: Centre de recherches mathématiques - CRM via YouTube
Course Description
Overview
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.
Syllabus
Anna Beliakova: Algebraic presentations of 4- and 3-manifolds
Taught by
Centre de recherches mathématiques - CRM
Related Courses
Real Analysis IIIIT Palakkad via Swayam Analysis II Video Lectures
YouTube Manifolds
The Bright Side of Mathematics via YouTube Manifolds, Classification of Surfaces and Euler Characteristic - Differential Geometry
Insights into Mathematics via YouTube Neural Manifolds - The Geometry of Behaviour
Artem Kirsanov via YouTube