Two submanifolds X and Y in an ambient space M intersect transversally if, for all p element X intersection Y, T X_p + T Y_p = {v + w:v element T X_p, w element T Y_p} = T M_p, where the addition is in T M_p, and T X_p denotes the tangent map of X_p. If two submanifolds do not intersect, then they are automatically transversal. For example, two curves in R^3 are transversal only if they do not intersect at all. When X and Y meet transversally then X intersection Y is a smooth submanifold of the expected dimension dim X + dim Y - dim M.

homology | homology intersection | Sard's theorem | submersion | vector space orientation