Officially the following topics will be covered

Vector spaces; algebras; topological spaces; simplicial homology; homotopy groups; differentiable manifolds; vectors and tensors; calculus of exterior forms; Stokes’ theorem; conservation laws and de Rham cohomology; parallel transport; connection and covariant derivative; geodesics; curvature and torsion, geometry of spacetime

These are all necessary for being able to follow the recent literature in mathematical physics.