We present a formula describing the action of a generalised Steenrod operation of ℤ2-type  on the cohomology class represented by a proper self-transverse immersion f: M↬X. Our formula depends only on the Umkehr map, the characteristic classes of the normal bundle, and the class represented by the double point immersion of f. This generalises a classical result of R. Thom : If α∊Hk(X;ℤ2) is the ordinary cohomology class represented by f: M↬X, then Sqi(α)=f∗wi(νf).
 Adams, J. F.1978Infinite Loop SpacesPrinceton University PressPrinceton, New Jersey.
Adams, J. F.1978Infinite Loop SpacesPrinceton University PressPrinceton, New Jersey.)| false