Mersions of Topological Manifolds
David B. Gauld · Transactions of the American Mathematical Society · 1970
We here generalise the immersion and submersion theorems of Smale, Hirsch, Haefliger and Poenaru, Phillips, Lees, and Lashof, giving a relative version in the case of mersions of topological manifolds. A mersion is a map of manifolds ${M^m} \to {Q^q}$ which in the appropriate local coordinate systems has the form ${R^m} \to {R^q}$ of the standard inclusion or projection of one euclidean space in another. Such a mersion induces a map of tangent bundles satisfying certain properties. In this paper the problem of classifying mersions is reduced to that of classifying such bundle maps.