Topology of Lagrangians Via Open-Closed String Topology

The topology of Lagrangian submanifolds in the standard symplectic vector space 𝐶𝑛 is a fundamental, yet poorly understood, problem in symplectic topology. A related question, known as Maslov class rigidity, concerns constraints on the Maslov classes of Lagrangian embeddings in 𝐶𝑛. I will describe a new approach to these problems based on ideas from open-closed string topology. As applications, I will present new results on these questions, extending classical theorems of Viterbo, Cieliebak–Mohnke, Fukaya, and Irie.