Bordism, Genera, and QFT

Bordism is an equivalence relation on manifolds and has been a powerful tool in algebraic topology for the last 60 years. A genus is a $\mathbb{Q}$-valued function on equivalence classes of manifolds (actually it's a ring homomorphism); genera have played an important role in 4-manifold topology, index theory, and homotopy theory. In this talk, I will recall the cobordism ring and discuss generators in terms of explicit manifolds. Next, I will introduce some examples of genera and then recall a general construction due to Hirzebruch. Finally, I will present an interpretation of genera through the lens of quantum field theory and share some recent computations.