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  • 1 School of Mathematics, Alan Turing Building, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
  • 2 School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, UK
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We present a formula describing the action of a generalised Steenrod operation of ℤ2-type [14] on the cohomology class represented by a proper self-transverse immersion f: MX. 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 [13]: If αHk(X;ℤ2) is the ordinary cohomology class represented by f: MX, then Sqi(α)=fwi(νf).

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