2K-REGULAR MAPS ON SMOOTH MANIFOLDS

A continuous map f : X --> R(N) is said to be k-regular if whenever x( 1),...,x(k) are distinct points of X, then f(x(1)),..., f(x(k)) are li nearly independent over R. For smooth manifolds M we obtain new lower bounds on the minimum N for which a 2k-regular map M --> R(N) can exis t in terms of the dual Stiefel-Whitney classes of M.