Integration on manifolds refers to the process of extending the concept of integration to more complex spaces called manifolds, which can be thought of as generalized surfaces. This process allows us to define integrals of differential forms over these manifolds, which is crucial for various applications in physics and mathematics. By generalizing integration, it becomes possible to analyze properties of functions and forms that behave well under smooth transformations, leading to deeper insights in geometry and topology.
congrats on reading the definition of integration on manifolds. now let's actually learn it.