Introduction To Differential Geometry And Topology In Mathematical Physics, An

Differential manifolds - preliminary knowledge and definitions; properties and operations of tangent vectors and cotangent vectors; curvature tensors, torsion tensors, covariant differentials and adjoint exterior differentials; Riemannian geometry; complex manifold; global topological properties - homotopy equivalence and homotopy groups of manifolds; homology and de Rham cohomology; fibre bundles and their topological structures; connections and curvatures on fibre bundles; characteristic classes of fibre bundles; index theorem and 4-manifolds - index theorem for manifolds without boundary; essential features of 4-manifolds.