Self-intersections of Immersions and Steenrod Operations

Details Self-intersections of Immersions and Steenrod Operations Self-intersections of Immersions and Steenrod Operations

2005-09-09

arxiv.org/abs/math/0509213v3

Mathematics

Algebraic Topology

10 pages; v3 final version, to appear in Acta Math. Hungarica

Scientific paper

We present a formula describing the action of a generalised Steenrod operation of $\Z_2$-type on the cohomology class represented by a proper self-transverse immersion $f\co M\imm X$, in terms of the equivariant double points of $f$ and the characteristic classes of its normal bundle. This generalises a classical result of R.\ Thom: If $\alpha\in H^k(X;\Z_2)$ is the ordinary cohomology class represented by $f\co M\imm X$, then $\mathrm{Sq}^i(\alpha)=f_* w_i(\nu_f)$.

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