Definition

If (U,φ)(U,\varphi), (V,ψ)(V,\psi) are two charts such that U∩V≠∅U \cap V \neq \emptyset, composite map ψ∘φ−1:φ(U∩V)→ψ(U∩V)\psi \circ \varphi^{-1}: \varphi(U \cap V) \to \psi(U \cap V) is called a transition map.

References

  1. J. M. Lee, Introduction to smooth manifolds, Second edition. in Graduate texts in mathematics, no. 218. New York Heidelberg Dordrecht London: Springer, 2013, p. 12.