The symplectic topology of cotangent bundles
In the present article the author starts with a brief review of the roots of symplectic geometry and then continues to discuss important questions of symplectic topology in its classical framework. These questions are aimed at understanding the interaction between the smooth topology of a manifold and the symplectic topology of its cotangent bundle. Objects of study in this investigation are (exact) Lagrangian embeddings, immersions and their deformations. The author introduces the main tools for tackling the questions posed, which amongst others include \textit{Floer cohomology} and the notion of \textit{Fukaya \(A_\infty\)-category}. At the end, the article provides a brief tour on the unrecognizability of symplectic manifolds.
scientific article; zbMATH DE number 5774738