Abstract
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.
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