The transition function of two charts (U,ϕ)(U,\phi)(U,ϕ) and (V,ψ)(V, \psi)(V,ψ) on a manifold MMM is the composition ψ∘ϕ−1:ϕ(U∩V)→ψ(U∩V)\psi \circ \phi^{-1}: \phi(U\cap V)\to \psi(U\cap V)ψ∘ϕ−1:ϕ(U∩V)→ψ(U∩V).