Transversality

Summary

Transversality is the condition that two submanifolds, or a smooth map and a submanifold, meet in general position. At each meeting point their tangent spaces together span the tangent space of the ambient manifold. Transverse intersections are again submanifolds, of the expected dimension, and they persist under small perturbations. Transversality is the basic notion of general position in differential topology and underlies intersection numbers, degree theory and cobordism.