J. M. Lee p. 55 Introduction to Smooth Manifolds -- "it makes no sense to talk about a linear map between manifolds."
Why?
2026-03-31 18:48:54.1774982934
Linear maps between manifolds
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Because there is no algebraic structure (addition, scalar multiplication) on a smooth manifold with no extra structure. (E.g. what is addition on a 2-sphere? What is scalar multiplication?)
A linear map is a map that plays nicely with those structures.