Some topological tools
B.1 Forms and cycles: cohomology and homology
B.1.1 Differential manifolds, tangent and cotangent space
A differential manifold X of dimension d is defined as a space with local patches U(α) parametrized by local coordinates , glued together with smooth transition functions f(αβ) on the overlaps , schematically as
From now on we drop the patch labels, and the adjective “differential,” and simply ...