What Are the Betti Numbers of a Manifold? - Don Zagier - 2017

Explore the concept of Betti numbers in manifolds through this illuminating lecture by renowned mathematician Don Zagier. Delve into the fundamental aspects of algebraic topology as Zagier elucidates the significance and computation of Betti numbers, which provide crucial information about the topological structure of manifolds. Gain insights into how these numerical invariants relate to the connectivity and holes in different dimensions of a manifold, and understand their applications in various areas of mathematics and physics. Whether you're a student of topology, a researcher in related fields, or simply curious about advanced mathematical concepts, this talk offers a deep dive into an essential topic in modern geometry and topology.

What are the Betti numbers of a manifold? - Don Zagier - 2017